Will someone correct this letter?
 

I would be very grateful for any help. :) I'm going to Japan this fall and was asked to write a short letter of introduction to any possible host family.

はじめはして、キャロラインと申します。ウィッテンバ ー大学の三年生です。せんこは美術と日本語です。今、 オハイオに住んでいって、小さい市です。ウィッテンバ ー大学がオハイオにあるから、あまり旅行しません。だ から、留学できるから、うれしくています。でも、日本 語の三年生いるだけ、日本語で話すのがきんちょうにな ります。それで、日本でぺらぺらな日本語が話すのが習 うつもりです。
よろしくおねがいします。

My honest suggestion would be to send it as is. They will understand 95% of the content. It will be much more personable if you leave the mistakes.

For your studies, however, I might point out the following:

三 > Never hesitate to use Arabic numerals when writing horizontally. Japanese-learners use way too many kanji.

せんこ You can correct this. Hope you are not using romaji in your head. Those who do will end up writing ども、ありがと、ときょ、きょと、おさか, etc., which are all wrong.

いって Where are you going?　;) 　 いって and いて are two different words with two different pronunciations.

オハイオに住んでいって、小さい市です sounds awkward.
＞＞＞　オハイオ州の小さな町に住んでいます。

留学できるから、うれしくています　＞＞　留学ができ てうれしいです

日本語の三年生いるだけ This is the only part Japanese-speakers will not understand. What did you want to say here?

日本語で話すのがきんちょうになります　＞＞　日本語 で話すときんちょうします。

日本でぺらぺらな日本語が話すのが習うつもりです = awkward
＞＞　日本で日本語がペラペラになれるように勉強する つもりです。

Thanks for the help! :) As for Romaji, I don't use it, they've really beat the writing into me at school. lol. I always switch to Hiragana even when I don't mean to. Sooo, I just can't spell. lol

Oh, and as for 日本語の三年生いるだけ, I just changed the end to　だから. Is that fine?

I was just pondering over something related today while doing some translation—it's awkward because the first half the topic is "I" but the latter half the topic is a city, right? You aren't really supposed to mix topics within clauses linked by the て form, right?

Like
私は学校にいって、友達は床屋さんに行きました。
Awkward, for one thing, because the first half's topic is "I" while the second half is "my friend." Right?

If you mean the いるだけ part by "the end", yes. But it will not connect well to the main clause. Adding まだ at the very beginning wil solve this problem.　Avoid using だから in writing as it is very conversational. If you have learned なので, use uit instead.　

「まだ日本語の３年生なので、日本語 で話すときんちょうします。」

To be strict, native speakers do not say 「日本語の３年生」. We would say 「日本語せんこうの３年生」 or 「日本語科の３年生」.

Exactly.

This sentence is a very tricky one.

It is correct only if both the speaker and his friend had been together (even for a moment) before they parted and headed for their respective destinations.

A situation where the same sentence would be considered incorrect:
Teacher asks his 10 students what they did yesterday. Each one answers. You went to school straight from YOUR home and a Bob went to the barber's from HIS home. In this case, the same sentence would be considered incorrect by many. To say it, you had to know where Bob was going before he went there. You should not say it if it is only today that you found out where he went yesterday.