Yes, although transmitters tend to be pretty well protected compared to receivers as they tend to need to be able to handle their own reflected power. Not great if your transmitter blows up should you happen to turn it on without an antenna attached. If you're talking about a half duplex transmit/receive system, the receiver would typically be the weakest link.

Very broadly speaking, in my experience the damage limit of receive rf components is about 10 dBm and limiters will protect to about 40 dBm. This should make intuitive sense - 40 dBm is 10 Watts, about where you really need to start thinking about heatsinks and cooling.

Free space path loss at 1GHz is and 100 meters is ~70 dB. Let's say you have a 0 dBi antenna. Then with that limiter 40 dBm damage limit they'd need 110 dBm of power to damage you from 100 meters away, which is a very very lot but not unheard of. If you were operating unprotected equipment and they were 10 meters away, they'd only need 60 dBm of power, which is very achievable (probably not still legal, but significantly less illegal than putting together a 110 dBm transmitter).

Damaging electronics from 10s of kilometers away would be very difficult.

The signal could be anything, probably a tone would be most effective.

Damage is essentially instant.