Yesterday I've I decided to write entries in English - kind of a blog.

I hope, I can improve my English until my exams!

I was afraid I would be hungry, because I should have gone to the shop buying something to eat, but it had been already closed. (You were afraid in the sense of being disappointed, not fearful, so we add an explanation.)

I started looking around for people, who could lend me English books.

I hope, that it'll still be there, if I'm going back.

I hope I can improve my English until by my exams! ["by" means "by the time" (my exams come)]

Today I woke up really late.

buying to buy something to eat, but it had been was already closed.

However, I can order a pizza or some Chinese food, too. [if you mean generally everyday you can order pizza or some Chinese food, this is correct. If you meant yesterday you were still able to buy some pizza or some Chinese food, then "..., I could still order..." is the way to go :-)]

I hope, that it'll still be there, if I'm going back.