Heatsink tabs are heat sinks keep the switches from overheating at higher loads. It’s fine to remove the tabs, but if you do, the switch cannot handle as high a load. The exact change will be detailed in the manual for the specific model. Here’s just an example:
The airgap tab or airgap switch is a physical tiny switch, typically on the bottom of the device. When you pull it, you create a physical disconnect between the device and the circuit branch. So it’s essentially like unplugging the cord from the outlet. pushing it back in restores the power.
That said, for some weird reason at least the older models of GE switches didn’t always fully reboot if you just use the airgap. Some people found they had to cut power at the circuit box instead. There has been much discussion of this in the forums over the years. But usually just the airgap switch is enough.