One is a wooden American Girl nightstand. I don't want the glue to show. Should I use wood glue (or would that show), clear tacky glue, superglue or something else?

The other is a polymer sculpture - my cleaning woman broke a couple of fingers off the sculpture. I'm not sure if I should glue them - or if it needs to be done by the artist - remolding the fingers with more polymer clay. I'd like to avoid the latter if I can fix it well - bc. sending it back to the artist is not just more time and money - but each time these are shipped back and forth there's a chance of them breaking in transit. The first time I bought one of these sculptures, it arrived broken. We had it insured but the artist wanted to fix it herself. She did - and once again it was broken in transit back to me. I think the Washington DC postal workers are rough on packages - but there's no telling for sure where the breakage occurred. Anyway - I'm not sure if there is an appropriate glue for something this tiny - that definitely has to hold well and be invisible.

Any good rules of thumb about which glue for what purpose?

Thank you.
Lynn.