In Framing Frame, will the guards get alerted if they see a missing painting

The only way to prevent the gas is by killing the cops on the roof, which get dropped via a chopper. Bane warns you when a chopper is inbound, so get up there and liquidate them.

If there is already tear-gas, you cannot "switch it of". I searched for quite a bit, but cannot find something that states that you can get rid of tear-gas.

The rules for this were changed 5th of March 2014 (emphasis mine):

Every player with the Dominator skill can now dominate one guard each at the same time. But apparently the old pager operators got fired, and more experienced operators are taking over. So clear your throats, and get ready to answer the pager as soon as you dominate a guard.

So one dominated guard or police officer per player with dominator. That means no, you cannot dominate multiple guards at once. You will need a friend to help.

Before this change the rule (which console and unpatched versions might still follow) was one dominated guard or police at a time. Want another one? Kill the existing one.