"Please, you are welcome!"
Translation:בבקשה, אין בעד מה!
You are absolutelly right about Russian. The exact American/European English equivalent/translation of не за что or אין בעד מה would be: " There is nothing to thank me for". It is a bit long compare to Hebrew and Russian, and here is English is not flexible. I want to stress that this is a translation of a concept relayed by the sentence and not an attempt to translate word by word, as in Hebrew and in Russian it is a bit idiomatic and there is more being implied than being said. Therefore this is a literature and not machine translation l am giving here.
Also for everyday common unformal use we say among friends and family "bekef" בכיף which means "with joy" or more literaly "with fun" So someone says TODA and you say back BEKEF, תודה בכיף A little more formal answer is בשמחה "BESIMKHA" KH=ח. Which also means "with joy" or literaly "with happiness" This you can use if you want to be a little bit more polite and formal, but yet it is not realy formal answer, but will be accepted as polite answer in most cases. Actually these words can replaces בבקשה in most cases but considered not formal
Yes, there are more then one uses for בבקשה, of course. First of all is "please" when you ask someone for something in a polite way you say "please" of course. Another is like saying "you are welcome". And less common but very polite is if someone ask you if he can do or use something you answer with בבקשה. And if you want to emphasize you make it double בבקשה בבקשה like "go ahead". "Can I use the phone please?" You can answer politely בבקשה. Maybe i can think about somemore uses but maybe these are the most common IMHO. Maybe some other natives can add to it. BEVAKASHĀ, the accent is at the end of the word