Is there any problem?
There is any problem?

I think in English both versions are correct.
Well, I don't think so. If you mean to ask something, the first option is only correct. The 2nd one is worded like a simple narrative sentence, not a question. If you reinforce it with questioning intonation, you'll get either a slangy question that is commonly used only by uneducated people or MAY be used by ordinary people in CERTAIN circumstances (fooling around, acting, etc). Or you can get a rhetoric question, that in fact doesn't need an answer.