Do microwaves cook from the inside out?

No. Microwaves (not microwave ovens, the actual waves) penetrate the surface of food easily. They heat the inside of your food at the same time as the outside. Compared to a conventional oven, which heat from the outside in, microwaves are much faster.

Effectively Microwave Radiation does Heat the interior of an Object First and Hotter than the outside. I once overcooked Cookies in a M.W. Oven. They were burned to a CHAR inside but looked fine on the outside.

Likewise, if you walked in front of a RADAR Antenna (Microwave Source), you could FRY your internal organs yet look ok on the outside.