Before you buy anything find out what you need. Possibly all you need is a new bottom bracket.

Also a whole 105 group is $400, so don't spend $500 on a partial group.

Really nothing can go wrong with cranks. Chainrings can wear .... they get what is called "shark-fin" instead of having a flat-topped triangle profile, and the chain will start slipping.... Not what you are describing.

The cassette will wear the same way ... but if your chain isn't slipping, it might be fine.

Your chain will stretch a little. If you maintain it all you will get 3-5000 miles from a chain.

The only thing that would make the cranks turn stiffly would be bottom-bracket problems. I don't know what kind of bottom bracket you have, but likely you would need to buy a cheap tool, spin out the old one, thoroughly clean the threads of the frame, and stick in a replacement. You can get the tool and BB for $50-$60 if you look around.