If someone apologizes for making a mistake and says "bocsi" (this is the informal form of "Bocsánat(ot kérek)!", you can say "Semmi baj." If someone asks you for something and addresses you with "Bocsi..." (again, informal), you can respond with "Tessék?" or "Igen?" (the former is considered to be more polite).

It depends on the situation. Hungarians tend to say 'bocsi' (informal of bocsánat) both for 'sorry' and 'excuse me'. In the first case you can say 'semmi baj' (no problem), while in the second it is 'tessék' (please).

I am not an expert on Hungarian, im still learning it , but what about to say just ,,nem baj ,, or minden rendben for example =) ?

Yea, if s/he sais it because of like stepping on your foot or causing stg inconvenient to you, you can also reply "nem gond" which means "nao faz mal".