I have a question guys. Can large monsters stand off map, like 4 spaces of Their base on Map and 2 off to be able to stand on the tile?

No, the whole base needs to be on the map.

No, the whole base needs to be on the map.

Correct, At no time can a monster's ( or figure's for that matter) base be off the map. If it's a question of Reinforcement then the monster has to place his base on the closest possible open spaces to the spawn point.