How hot does it get underneath the unit?
The unit is raised on the legs and the bottom is double wall. I assume it gets hot to the touch but the legs raise the unit up off the surface.
Should I plan on a wooden board to put under it or some other type insulator?
I would not think it would need it but maybe one large 14X14 ceramic tile would be a good idea. I use mine outside on a glass top patio table so I am not concerned.
If I set it on an outside countertop (Laminate) would it get hot enough to delaminate the top?
I don't think so but again maybe a large ceramic tile underneath to protect your laminate top regardless. I would be concerned about any grill sitting on a laminate countertop.