Why are there twelve month in a year?

Notes:

"synchronize" isn't incorrect, but another word that most people would use is "coincide".  To coincide with something means to "go along with", essentially the same as synchronize but used more often in situations were you're out of control of one of the things you're trying to synchronize.

"plant" as a verb means "to place into the ground".  Very easy to remember, "You plant a plant in the ground"  (verb and noun).

Your English is good, keep practicing and expanding your vocabulary : )

Indian movie

I watched an Indian movie with my host family.  I can't understand Hindi, but there were English subtitles I could read. I was very conscious of them because they didn't sync with the actors' voices. It was funny.

This is a confusing correction.  By "They didn't adjust the actor's voices", I'm assuming you meant to say "they didn't sync with the actors' voices.".  As in the subtitles didn't match up with the words that were being said.

"sync" is short for "synchronize" (シンクロナイズ).  Synchronize means to happen at the same time. 

Note:

When deciding if you use "the" or "my" when referring to host family depends on if it's your host family, or someone else's.  Assuming it is the host family you are staying with, you would say "my host family".  If you were talking about a friend's host family, you would say "the host family" or "their host family" (either would be correct).

The way I would say the same thing:

I watched an Indian movie with my host family.  I don't know Hindi, but it had English subtitles.  The subtitles didn't sync with the actors' voices. I thought it was funny.

I hope that helps, good luck and have fun with your studies!

American jokes

Corrected:

I heard an American joke on a Japanese TV program the other day.
An American lady said this,
"I registered at an online dating site because I'm already 37 years old, not married, and have no children.
When I was viewing the profiles of registered men my dad's profile popped up. "

("no children" instead of "have no children" is OK, but it would be considered "lazy english".)

("While I was viewing the profiles" sounds better, however "When I was viewing the profiles" is acceptable.  Native speakers will say it both ways.)

Notes:

With English sentence structure, when you are listing more than two things you do not use "and" but instead make use of a comma.  Example: You would not say, "He is big and tall and strong and fast.".  You would say, "He is big, tall, strong, and fast.".  After the last comma, you include "and".  This applies to both written and verbal English.

Many nouns have plural forms.  Some are more tricky than others (in particular, when talking about animals).  An example given in this correction, when talking about more than one "man" it becomes "men".  The same applies with "woman" becoming "women".

Possessive nouns:

When you are referring to anything belonging to a noun (person, place, or thing) you simply add " 's " to the end of the noun to state the following word belongs to it.  Examples are "dad's profile", "Tokyo's buildings", "dog's bowl".

I hope these corrections and explanations help : )  Keep practicing, have fun, and good luck in your studies!

Poetry is good, but be mindful that a lot of poetry is intended to have a deeper (or different) meaning than what is written.  Sometimes impractical words will be used as metaphors and such.  It may not be the best for conversational understanding, but it can be great for comprehension of the language and vocabulary.  It really depends on the poetry, how it is written, and at what level of understanding you're at with the language.  In short though, yes it can help and if you're interested in it then read it.  If you come across something that just seams odd, look into the words or statements that seam out of place. Consider what else they could mean, or what they could symbolize.  Poetry could be a great tool for understanding metaphors and context of English vocabulary, I just wouldn't recommend it for early beginners of the language.

To put into perspective, even native English speakers will study poetry in university.  Consider it the ocean, it is beautiful on the surface with even more to discover when you look beneath it : )