Student or Learner
I can guess this stupid questions every newbie ask but I've no choice.
1. How to improve/learn grammar ? Are there any easy-to-learn articles on net ? Do you recommend any English grammar books ?
2. When I read newspaper or watch news/movies in TV I don't understand some words as a result I don't understand anything there. Are there any sites/books to improve my Vocabulary ?
I think you're going to get a long list of people telling you to go to their own sites. (I just started my own site for English learners, you can find it here.) But, I don't think you need a website to improve your English so much as you need time.
My advice is to try to learn one 'piece' of grammar a week and practice it as often as you can. You don't need to write anything to practice it, just start thinking of sentences using the grammar and ask youself 1) if you're certain you're using it correctly and 2) if you understand the different 'feeling' of the meanings.
For example: I encourage German students to spend a lot of time on "Have done" and "did" because it's different from the way they talk in German. So, if it's a trouble spot for you, start thinking of all the things you can say with each form, and think about the differences. When they become automatic--don't be in too much of a hurry--move on to the next thing you're having trouble with.
As for point number two: don't worry about the words you don't know. If you relax, there's a good chance you'll understand a lot of what's happening, even if you don't understand every word. If you watch DVDs, watch a DVD you already know in your own language in English. Then, even if you don't know the words, you know what they're saying and, eventually, something will click. You'll find your vocab growing without ever 'studying.' (I use this trick in German. Now there are words I know in German without knowing the English equivalents.)
Hope this helped,