If you’re concerned about the tabletop expanding and contracting, the traditional method of button fastener (or modern metal alternatives) is the way to go. Epoxy encasement of the will keep moisture out (as will most other finishes) but doesn’t stop heat.

Whilst your planks look relatively thin (the thicker the wood, the more likely it is to change shape as it dries) wood will do what it wants, so who can say if it’ll warp, or in what direction, so you have to try and design around that, and either hold it in position if it moves, or allow controlled movement. Traditional button fasteners will allow movement, but modern adhesive/fasteners combinations can hold significant stress.

The damaged sections of leg can either be redrilled deeper, or threaded inserts located within the damaged sections during a repair (dust and epoxy/filler/excise and new wood repair)

Their are many ways to skin a cat, and if you haven’t already read a book on table building and see what techniques you want to use.