College does not need to be capitalized unless you are naming a specific college i.e. My mother went to Ruthsberg College when she was 18 years of age. Notice how you capitalize it when it is as a title, such as Ruthsberg College (this is a made-up college). 

You do not have to place a comma after the word "English". In most cases (such as this) the comma is not necessary before the conjunction word "because".  You do not have to place the ending "ing" to the word "travel" for this sentence.

Replace "able" at the end of the sentence with the word in itself "comfort", this makes more sense for your sentence. You can replace "and easy to talk with other people" with "and with ease..."

"As" is more appropriate for this sentence than the word "a", and the word "to" before the word "traveling" is not necessary here.

I will rewrite your entry, and with red and bold letters will I input the mistakes I mentioned above (This _ means a space was added):

I am learning English_because I want to go to a college, travel with comfort, to find a better job, and with ease talk with other people. My native language is Russian, as I grew up in Russia. I enjoy_ traveling, to read, and to rest with my family.

Bonus Tip:

You can put either the word "with" or to" for the sentence "...and with ease talk with other people." or "...and with ease talk to other people." it still makes sense. You don't necessarily have to put "to" every time you're listing what you like to do. For example it is still okay if you put it like this: "I enjoy traveling, reading, and resting with my family." you may find a lot of books in the English language that do this. You can also put "to" before you even mention what you enjoy to do and it will still be okay. For example:

"I enjoy to travel, to read, and to rest with my family."

Notice how the structure of the sentence changes a bit. When you put "to before you list any of the things you like to do, that also changes how you put them each in the sentence. It wouldn't make sense to say, "I enjoy to traveling..." but rather "I enjoy to travel...". You put the word in it's nominative form--"travel"--instead of "traveling". Note here then you will also have to put the word "to" before the next thing in your list, i.e. "...to read, and to rest with my family.", as it makes much more sense like this.

It's also okay to add in the sentence the indirect object of which you like to read, i.e "...to read books". Or to make it more direct and add it's author, "...to read Be Perfect by Andrew Murray..." or to make it direct (and not adding the author's name), "...to read the book Absolute Surrender.".  You can categorize all the books by one or more authors, such as:

1. "...to read books by Andrew Murray..."

2. "...to read books by Andrew Murray and Sheila Walsh..."

I hop that helps you a lot! You're doing good in your English though, so keep on studying and pressing through anything that seems to difficult in the English language! Keep on studying hard and you will be great at speaking, reading, and writing in the English language! I hope that this has helped you in any way! Keep up the good work!

First notebook entry: Introducing myself

I am learning English because I want to go to college, to make travelling more comfortable, to find a better job, and make it easier to talk with other people. My native language is Russian. I enjoy travelling, reading and spending time with my family.

First notebook entry: Introducing myself

I am learning English, because I want to go to a College, traveling with comfortable (к сожалению, я не поняла это. Ты означаешь, что хочешь знать английский язык чтобы удобнее и эффективнee общаться с людьми за рубежом?), to find a better job, and to easily to talk with other people. My native language is Russian, and I grew up in Russia. I enjoy to travelling, to read, reading, and to rest spending time ("проводить время") with my family.

First notebook entry: Introducing myself

I am learning English because I want to go to a college, traveling with comfortable, to find a better job, and easy to talk easily with other people. My native language is Russian a I grew up in Russia. I enjoy to traveling, to reading, and to having some rest with my family.

First notebook entry: Introducing myself

I am learning English(no need for comma before because) because I want to go to a College. I also want to traveling with comfortably to find a better job. I would like to and easy to talk with other people freely. My native language is Russian, and I grew up in Russia. I enjoy to traveling, to reading, and to rest spending time with my family.