Is it possible to let it soak up oil on the back side
to prevent future breaking of other pieces?
first of all ~ you have some AWESOME carvings there !!
I am very envious of your craftsmanship to do such nice work
in just plain old construction pine. very nicely done !!!!
if I had something that nice with all that work you put into it,
I would use the strongest picture hanging hardware I could find
and also the appropriate drywall fasteners to match.
it sounds like you just drilled a hole in the back and hung them on a nail.
please expand a little on your hanging methods - that may be the
culprit of them falling off the wall.
Priority Number One is to stop them from falling off the wall !!!!
as for repairs, if you have good clean breaks, and recovered all the pieces,
just plain TiteBond II wood glue will work just fine and easy to clean up.
there is no need for epoxy or similar adhesives.
I see no reason to treat the backs with oil or other stuff. just the same type
of finish you used on the front for the back, and the same number of coats.
I do carved signs, and that is the rule of thumb to use equal coats of finish
on all sides and edges to "help maintain" the equilibrium of the piece.
again - very, very nice projects !!! hope to see more of your work in the future.
[and spend some time with a photo editing program to post some nice photos].
FootNote: if you are going to be a woodworker; especially a woodcarver,
learn how to make invisible repairs in your work !!!!