Where can i find the patch to play this game translated

Check The Whirlpool.

Play it translated? Translated to what? Theres a (E) and a (U) version of Prince Of Persia, are you wanting a Japanese version or something?

Is Arabian Nights the same as Prince of Persia?

Yes, the full title I believe is..... Arabian Nights - Prince Of Persia. If you look it up, there is no game called that for Genesis/MD, it's simply called "Prince Of Persia".
The one for Dreamcast however uses the full title.

I checked on gamefaqs, and there is no game called Arabian Nights for the Genesis. There is a jap Arabian Nights for the SNES though. Is this the game you want?