>> As for "embryos", I don't really know what exactly the word they use. I chose this word after looking up a dictionary. Can you suggest one?

The word 'embryo' refers to something which is not yet in its final form—it still must change into its final form.  The jewelry cast from a mould is already in its final form.  It will have the precious stones added, but its form will not change.

If you make something from a mould, whatever comes out is called a 'cast'.

>>  I hope you can tell me why "waiting for its coagulation" is wrong.

I said that it was a little wrong.  Coagulation is a process which occurs over a period of time.  So, what does "waiting for its coagulation" mean?  Waiting for it to start coagulating, waiting for it to be half-way through coaguating, or waiting for it to have finished coagulating?  I read it to mean the start of coagulation.  This is made clearer if you consider the following sentence:

"I am waiting for Tom to study English."

I would say the above sentence if I am waiting for Tom to start studying English.  To refer to the completion of study, I would say the following:

"I am waiting for Tom to finish studying English."

Therefore, I would write your sentence as follows:

"Then a jewelry cast is produced by pouring liquid gold into this mould and waiting for it to finish coagulating."

As I said, your grammar was fine.  Only the meaning was very slightly wrong.

>> I thought I can could omit "is" because I already used an "is" in the same sentence. Now I guess it is not acceptable.

Let me start a different sentence:

"After I have prepared the cake's base, it is adorned with chocolate and ____."

What do you, the reader, expect to come next?  You probably expect another ingredient such as 'strawberries'.  (The cake is adorned with chocolate and strawberries.)  If instead of a noun you read a verb, you may have to re-read the sentence.  

Now consider the following sentence:

"After I have prepared the cake's base, it is adorned with chocolate and is ____."

What do you, the reader, expect to come next?  You probably expect a verb phrase to follow.  Perhaps the cake is adorned with chocolate and is baked in the oven.  Or it is adorned with chocolate and cut into pieces.

The word 'is' signals that you are about to introduce a new verb or verb phrase.  In retrospect, a better word would have been 'then':

"After that, the cast is mounted with gemstones and then polished."

Now, this is the sort of edit which I should not have made.  Your sentence was not wrong.  If my comment has annoyed you or confused you, I am truly sorry.  Yet, in my defense, these small changes can make a real difference to comprehensibility.  When you next find yourself reading a sentence two or three times, think back to this comment.  A word like 'is' or 'then' can often be omitted, but doing so may cause the sentence to be harder to read.

After visiting the production line we went to the jewelry storehouse. Actually these jewelries the storehouse jewelry looked not did not look as beautiful as jewelries we saw on stores jewelry in a retail store because there was no elaborative elaborate adjusting adjustable light shining on them and all the jewelries jewelry were was just put there casually like they are cheap fashion jewelries jewelry. But they are were still beautiful, well designed and with perfect handy work handiwork. I think that it is a big dream for of every woman to be in a house like this, surrounded by glamorous jewelries jewelry, even without the permission to touch them. 

The most exacting exciting [14] part is was visiting the diamond storehouse. There are all diamonds everywhere, on shelves, and on desks, all with perfect cut and of high quality. Of course we cannot see the cut of diamonds with our bare eyes. The manager picked a highest level diamond [15] and put it under a microscope so we could see the hearts and arrows of it. It is was so beautiful, so bright. I immediately covered my face with a silk stocking [16] and robbed stole all the diamonds. (Okay, I am joking.)

The tour was amazing. I am kind of [17] starting to love my job.

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[14] I am presuming that you typed this incorrectly.  If you did indeed mean to type 'exacting', you would need to elaborate why the diamond storehouse was the most exacting part of your audit.

[15] The phrase "a highest level diamond" sounds strange, unless it is a term used in the industry.  I feel that the following would be more natural:

"The manager picked a diamond with the highest-quality cuts and put it under a microscope so we could see the hearts and arrows of it."

[16] Sheesh, only a diamond thief would use a silk stocking.  Bank robbers use simple nylon stockings.

[17] Phrases like "kind of" and "sort of" add no meaning.  In fact, they usually dilute your meaning.  Which of the following sentences sounds more emphatic?

"I am kind of starting to love my job."

"I am starting to love my job."

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Don't be alarmed by the number of corrections I have made.  When I edit an essay on Italki, I aim to make a 10% to 20% improvement.  Anything more than that may be overwhelming to the student.  For people whose English is poor, I make far fewer corrections, to help them get the basics right.  For people whose English is strong, I have to make more corrections, and more subtle corrections, in order to suggest improvements.

When we are were visiting the production line we found that the corridor is sticky. The manager explained that is because they use sticky floor mats to stick collect [6] gold powders [7] or other noble metal powders such as platinum powders, which then are then gathered and reused. Gold is expensive and cannot should not [8] be wasted. 

It was new for me to actually [9] see exactly how exactly a [10] jewelry is made. First a metal mould is made with a wax model which looks exactly the same with as the jewelry that is going to be made. Then an embryonic [11] form of jewelry is produced by pouring liquid gold into this mould and waiting for its coagulation [12]. After that, the embryo is mounted with gemstones and is [13] polished. Of course the real processing course production process is more complex than that.

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[6] Writing "sticky floor mats to stick gold powder" is okay, but somewhat redundant. If you change the verb to 'collect', it better expresses the purpose of the sticky mats.

[7] 'Powder' is an odd word.  When talking about a single type of powder, the noun is uncountable.

"She has a lot of washing powder."

"She has a little washing powder."

However, when talking about different types of powder, or different collections of powers, the noun is countable.

"This washing powder is very cheap."

"These washing powders are all very cheap."

[8] 'Cannot' would mean it's not possible to waste the gold, which is clearly not the case.  The phrases "should not" or "must not" would be correct here.

[9] It is not necessary to use both 'actually' and 'exactly'.  The following sentences convey the same meaning:

"It was new for me to actually see how jewelry is made."

"It was new for me to see exactly how jewelry is made."

Your sentence was not wrong, but it's not necessary to use two 'amplifying' words. To see what I mean, the following sentence uses three amplifying words:

"It was new for me to actually see exactly how jewelry is really made."

Using three amplifying words makes the sentence very clumsy.  Using two amplifying words makes the sentence a little clumsy.  One amplifying word is enough.

[10] 'Jewelry' is uncountable.  If you want to refer to a single item of jewelry, the phrase is "an item of jewelry".  In your sentence, you can simple say, "It was new for me to see exactly how jewelry is made."

[11] Is that the technical word they used?  If not, 'embryo' is probably the wrong word.

[12] There's a slight problem with saying "waiting for its coagulation".  The grammar is fine, but the meaning is a little wrong.  However I feel that I'm making far too many comments.  Let me know if you want yet another comment.

[13] Let me know if you don't know why I have added this verb.

Diamonds! Diamonds!

A few days ago I visited to [1] a jewel-crafting [2] factory as an intern to assist my colleagues’ work. The Indian manager offered us a tour in this of the [3] factory. In India, there are some families which do jewel-crafting management [4] from generation to generation, like a family business. That’s why in this kind of factory the manager is usually an Indian.

The factory belongs to a European company. It makes jewelries jewelry [5] for luxurious brands. The exact names of these brands are secrets but we know they are front-line luxurious brands. It also makes jewelries jewelry for rich people in Middle Eastern countries.

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[1] Either of the following would be correct:

"A few days ago I visited a jewel-crafting factory."

"A few days ago I went to a jewel-crafting factory."

But "visited to" is not correct.

[2] This is a compound adjective which should have a hyphen.  As a guide, if the description goes before the noun, a hyphen is required.  In the following sentences, the noun is highlighted:

"I went to a factory which crafts jewels." (Description after the noun.)

"I went to a jewel-crafting factory." (Description before the noun.)

If you omit the hyphen, the sentence will usually still make sense.  Yet, if you're preparing for an IELTS or similar exam, you may get a bonus mark for properly hyphenating a compound adjective.

[3] Grammatically, it's fine to say "a tour in the factory".  That makes perfect sense.  Nonetheless, a native speaker will say "a tour of the factory".

[4] The phrase "do jewel-crafting management" sounds very odd.  A native speaker would never say that someone "does management".  The word 'management' is a noun, and you don't 'do' a noun.  Either of the following would be more natural:

"There are some families who work in jewel-crafting management from generation to generation."

"There are some families who work as jewel-crafting managers from generation to generation."

[5] 'Jewelry' is uncountable.  As examples:

"She has a lot of jewelry."

"She has a little jewelry."

"She bought an item of jewelry."

"She bought two items of jewelry."

Diamonds! Diamonds!

A few days ago I visited to a jewel crafting factory as an intern to assist my colleagues’ work. The Indian manager offered us a tour in this factory. In India, there are some families which do jewel crafting management from generation to generation, like a family business. That’s why in this kind of factory the manager is usually an Indian.

The factory belongs to a European company. This factory It makes jewelries jewelry  for luxurious luxury brands. The exact names of these brands are secrets but we know they are front-line luxurious luxury brands. The factory It also makes jewelries for wealthy rich people in Middle East. countries. rich can imply new money and wealthy implies mature elegant clientle

When we are visiting the production line we found that the corridor is sticky. The manager explained that is because they use sticky floor mat to stick gold powders or other noble metal powders such as platinum powders, which then are gathered and reused. Gold is expensive and cannot be wasted.

It was new for me to actually see how exactly a jewelry is made. First a metal mould is made with a wax model that which  looks exactly the same as with the jewelry that is going to be made. Then an embryonic form of jewelry is produced by pouring liquid gold into this mould and waiting for its coagulation. After that, the embryo is mounted with gemstones and polished. This is a simlified description Of course the real processing course is somewhat more complex than that.

if my edit has some value I can continue when I have more time :)

After visiting the production line we went to the jewelry storehouse. Actually these jewelries looked not as beautiful as jewelries we saw on stores because there was no elaborative adjusting light shining on them and all the jewelries were just put there casually like they are cheap fashion jewelries. But they are still beautiful, well designed and with perfect handy work. I think that is a big dream for every woman to be in a house like this, surrounded by glamorous jewelries, even without the permission to touch them.

The most exacting part is visiting the diamond storehouse. There are all diamonds, on shelves, on desks, all with perfect cut and high quality. Of course we cannot see the cut of diamonds with our bare eyes. The manager picked a highest level diamond and put it under a microscope so we could see the hearts and arrows of it. It is so beautiful, so bright. I immediately covered my face with silk stocking and robbed all the diamonds. (Okay, I am joking.)

The tour was amazing. I am kind of starting to love my job.