I'll take you up on it! How the hell can a student connect those prepositions to any type of reality!? I could find a way but it would be abstract hehehe

"to take up [something]" = to accept what has been laid down, in offering. The phrase probably started out as "I will take up your offer of help." But English evolves quickly and according to very strange invisible rules. :) so ... "to take [someone] up on" = to accept what [someone] has metaphorically laid down in offering.

Yes it does.

"I decided to take you up on your offer". This means you will accept their offer, whatever it is. It might be an offer to help, an offer to lend me some money, an offer to let me borrow a bed because I have guests or company coming and I don't have a place for them to sleep. "I will take you up on your offer", "I thought about it, and I will accept your kind offer".