First notebook entry: Introducing myself

Hi.
I'm Nana.
I am learning English because when I go to foreign country, I want to speak English with a lot of people.
When I went to Araska, I felt that everyone were friendly and cheerful.
So I want to make friends.

First letter of names is always upper case.
Usually you'd either say "go to foreign countries" or just "go abroad".
Also, if by Araska you mean the northern-most state of USA, it's spelled Alaska - though for all I know, Araska could also be a place (in which case I imagine telling the 2 apart would be difficult using only Katakana).

Other than that, I don't think you made any mistakes. A few things that could make it seem more natural, but that's something you pick up only through years of experience.