That's a veneering hammer (not actually a "hammer" in the
ordinary sense at all in that it is not used for striking.)
It is slid along the surface of the veneer to distribute the
glue, and better bond the veneer to the substrate.
All the best,
For removing broken wood screws, as others have said. CCW because, as
with a LH drill bit, that gives you two chances to remove a broken
screw. If the teeth catch on the screw and back it out, so much the
better. If not, they will remove a plug of wood with the screw in it.
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