I try to learn English, because it's useful and interesting. -> I try to learn English because it's useful and interesting.

This one was perfect except you didn't need the comma in between the two phrases.

I want to be up to day. -> I want to be up to date on things.

The idiom is 'up to date' and you should probably specify what you want to be up to date on otherwise your readers or listeners won't know what you're talking about.

Besides them foreign languages includes a lot of things that catch. -> I'm not too sure what you mean by this so I don't know how to go about correcting it, sorry.

But anyways, good job! ^_^

First notebook entry: Introducing myself

I try to learn English because it's useful and interesting. I want to be up to date on different things.  Besides them foreign languages includes a lot of things that catch my attention)