Origin - can i do a copy of my game and bring it to my friend?

Yes you can, ive done that lots of times, though i recommend you to use an external harddrive since some games are pretty heavy...

After that you need to tell his origin that you want to install the games exactly where you put the files, Origin will try to download again the game ignore him (tell them to go all the way and download it), because after a while he will realize he has all the files and will validate them like Steam does... (because Origin will try to download the game again you will need the double of hard drive size of the games, because it thinks that you dont have the game at all and need the space...)

Sorry for my english too ;)

Możesz, zrób kopie folderu z grą oraz wpisów rejestru ;p

Yeah, you can ;D

Yeah you can. Better method than mentioned is you start downloading game, let it download few MBs. Pause download. Go to the folder where game started downloading, add files from your friend and resume download on Origin, and voila you're done! :D