Songs are really good.
Your English is excellent: after all, you live in the Ukraine!
Think about your audience. Is it fellow Ukranians? If so, your English is fine.
If you are aiming towards the UK - you are not bad. A lot of Brits sing songs that are next to impossible to understand.
If you are aiming towards the USA - you need to study some key things, like choosing more wide vowels (copy from TV).
At present, I think you sound like a European who speaks English influenced by a British teacher. Mixed with some American English, which is common for rock music.
Of course, the "W" sound is tricky, and you need to decide how you will make it come across. Some speakers put an "H" sound in front to help to form the sound.
You are far better off making something of being Ukranian, and singing English with a distinct Eastern European accent. There have been Europeans who have made big careers for themselves in the USA for certain, keeping their interesting accents: just a touch.
A person who kept her accent and made it big was "Nico" - who was Swedish, I think. 1960s.
http://www.youtube.com/watch?v=FjjDmX9Tkss
Watch her sing "Femme Fatale." You may not understand that we Americans, especially heard her distinct Northern European accent: and the crowds loved her!
Your vowels can sometimes be longer.
Your consonants sometimes need to be more clear, similar to how you would speak them in your own language.
Oh, and the word "pretty" is pronounced "Pritty" (rhymes with Kitty). Don't say "preety" - that doesn't sound good.
good luck