First go in Korean...

오늘은 12월17일이에요.

예요 is used after nouns ending in a vowel.

이에요 is used after nouns ending in a consonant.

오늘 선물(들)을 사고 오빠를 만났어요. OR 오늘 선물을 샀어요. 그리고 오빠를 만났어요.

The plural (들) in Korean is actually not used that often, except when talking about people - that's when I see it being used most. So you could omit it.

To say "and" between verbs (including adjectives), first look at the dictionary form. Remove 다 and add 고.

예)

먹고 마셔요 - eats and drinks

공부하고 노래했어요 - studied and sang

미국에 살아요.

아/어/여서 is used to mean "so". But saying "I live in America so I go to college" doesn't really make any sense. Unless you think the U.S. is king of the world and other countries don't have colleges...

대학교에 가요. 대학교에 다녀요.

대학교 was misspelled.

Use 에 with a location and 가요 to mean "go to". 에 in this case means "to".

However, when you say it like this, it sounds more like you are actually going to a college. What you mean by "go to college" is that you attend college.

다니다 - to go somewhere regularly, to attend

It is also used with 에 to mean "go to regularly" aka attend.

So...대학교에 다녀요 is what you mean.

한국어를 배워요(공부해요/공부하고 있어요).

"공부하다" is used more often when talking about languages, but 배우다 is okay to use too.

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Excellent! Hope to see more from you :)

First go in Korean...

오늘은 12월 17일 이에요. 오늘 선물들 사고 오빠 만났어요. 미국에 살아요. 대학교 다니고 있어요. 한국어 배워요.