Bung:

 

"didn’t have a record of the size." to me is code for mattwnz's supplier originally had someone else making the cabinets.

 

If that is a bead of silicone between top and tile I see no reason that the tiles would get damaged removing the top. 

 

Depends on the grout and the trim looks like it has been installed tight to the vanity. Without cutting out the silicone you won't really know.