The rules state that amphibious assaults happen from the In Shore box. Is it safe to say that an Amph can also launch an amphib assault on a beach hex in the same sea zone from an all sea hex or a port?
No, it must launch from the In Shore Box.
Can units use the mech bonus to get an extra advance after combat hex in DMZ fortified hexes? It seems like the fortified hexes would restrict AAC like other tough terrain.
EDIT: I was too short with the answer. The "yes" was intended as a response to your second sentence. So, the answer to your actual question is "No, fortifications deny the second hex of advance."
Just to verify, when the first US/UN reinforcement is listed for GT2, you roll for its arrival in the Reinf Phase of GT2? And the reinforcements wouldn't move until GT3?
Correct. You place them on the map in the turn listed.