Reroof or tear off question

Is there a way to tell if the roofer did a reroof over exciting shingles vs a tear off then re roof?

For an experienced roofer it’s very easy to tell but not for an average homeowner. Check around the edges of the roof if you can see additional layers. However additional layers can be hidden under new metal or something like if someone wants to hide them.

Test cut or pull a couple shingles.

If they did a reshingle not a tear off and reinstall, would they be able to put new underlayment like a synthetic underlayment?

Yes, it is possible to cover old shingles with new underlayment. What is the reason you suspect they didn’t tear off the old roof?