How can I build and attach new plaster hands for a statue?
Your intention to salvage the statue is well placed. However, as already stated in a comment, your biggest enemy here is the fact that the structural integrity of the statue is affected, and therefore not reliable.

Before fixing the details, you should make sure that the statue can survive the repairs, instead of completely collapsing together with said repairs.

To verify the extent of the structural damage, you should carefully remove everything that can be removed - as in "disassemble the statue". You will understand better the skeleton it was built on (I see some wood "stick" inside the arm). Make lots of pictures, number the fragments...

Be sure to have good glue, compatible with the material of the statue.

And I would fix the base, before anything else. Otherwise, the base will allow the entire statue to be destroyed at some time later. Even a small accident will render all previous work useless, while trying to fix the base.



Bottom line: this appears to be a not-so-easy task. Even if it is not worth hiring a professional to do all the work, you may still contact a local professional for some advice - he will be able to see what cannot be seen in a picture.



Disassembling should not scare you too much - the statue needs a new layer of paint anyway - at least after de-molding and removal of exfoliated paint.