I don't think there are any simple ac questions myself...

The thing inside the box is the evaporator... where liquid refrigerant is let out in a spray and changes to vapor... adsorbing heat.... thus cooling fins...

It sounds like maybe the sensor on the dash,,,if you have one,,, might be dirty... and thus not responding quickly enough...

There are other things which can be going on ...so you may have to do more describing for us to be able to narrow it down...