Had a temp crown crack can that ever take a part of the remaining tooth with it?

Yes: Hopefully not, but yes it can happen. Best to go back to your dentist to check things out and make you a new temporary.

Potentially, yes: Temporary crowns are used with the intention of protecting the prepared tooth while a permanent crown is constructed in a lab. By definition, a temporary is not meant to last long term and sometimes falls off easily. As long as the tooth underneath is still intact, you are okay. If the tooth has broken off with the temp crown, then this seriously affects the success rate. See your dentist, soon.

Can/unusual: Temp crowns are usually made of acrylic and cemented w temp cement. Acrylic can crack easily if thin, and the temp cement will allow dislodgement w/out tooth damage. However, if stronger cement is used. And if the temp crown has great retention, then it is possible some tooth could fx with the temp, especially if there is an underlying crack in the tooth.

Not usually but can: Usually the temporary crown is the weakest link in the chain, so to speak, so that when the temporary crown breaks, the underlying tooth is still intact. However, it can and does happen that when the temporary crown breaks or comes off, it takes some tooth structure with it. Be careful not to eat hard and sticky foods if you have a temporary crown and see your dentist to have it evaluated\remade.