coping is a term from restorative dentistry and refers to a Zahnstumpfkappe or provisorische Hülse; often used with implants. So your surgical index coping could be s.th. like a chirurgische Index-Kappe. (Index = Index).
Contra angle = Kontrawinkel (source for this and all of the above: FDI Lexicon of English Dental terms; FDI being Fédération Dentaire Internationale; this is their offical dictionary).
I'd probably use "Antrieb" for the various terms with "drive" in it (I imagine that you might find a lot of those terms in a good technical dictionary like Ernst). The links listed below are rather old (it's been a while that I did anything in the field of dentistry), and they may not necessarily apply to what you're looking for but you may wish to try them anyway - maybe they'll lead you to a useful site!