A couple of days ago I bought Torchlight from they're official site and they gave me a serial number. Would there be any chance that I could acquire Torchlight here on GOG by sending someone my serial number??
I remember GOG did something similar with the other game here.

No, if you haven't bought it from GOG, you can't get it here for free.
Only for the Witcher games can you get GOG backups if you've bought them somewhere else.