Bill Tindall, E.Tn.
1. Where is a good source for bird’s eye maple veneer to attempt a color match?? Certainly Wood for the veneer But you will not get a color match without stain. New maple is not going to look like old, finished maple for decades.
2. Recommendations on how do I scrape/pry the existing partially loose panels off? Probably just a heat gun will work. Steam from a kettle definitely will work
3. Flatten whatever selected new veneer I find with heat? Unlikely to be necessary. Veneer has to be exceedingly lumpy to require flattening
4. I do not have a hot glue pot so what glue? White or yellow are fine
5. What don’t I know enough to ask? You are not going to learn enough to be successful just by asking on a Forum. What you want to do is not trivial. Some mentoring would be helpful.