The power available is not enough, and the breaker on that circuit must be too large a rating or you would be having to re-set it. That is a fire hazard.....
There is a reason the electrical code is actually produced by the "National Fire Protection Association" (NFPA)........... bad wiring causes fires.
Better find a new space, or practice at very low volume...... with different equipment.
As for amp damage....it depends on WHAT the equipment is, and how it is made.......
A normal SS analog amp with transformer is pretty "OK" in general... they draw less and less power as the voltage goes down, and eventually quit or sound so bad you'd know not to use them.
Most tube amplifiers will have bias that isn't overly affected by low voltage, but SOME might be so made that bias would be reduced at low line in a way such as to possibly damage tubes.... not overly likely, but possible.
Amps that have a switchmode power supply, i.e. lightweight amps, CAN (not all do) draw MORE current as the voltage drops..... and may not quit until voltage is below 90 VAC (for US). probably won't damage the amps, but may heat the wiring quite a bit, which can be a fire hazard if the wiring is bad/poorly protected.
Bottom line there is that if the amp isn't sounding bad, it probably isn't being damaged.
I've seen some bad-wiring....... In our house a previous owner added an outlet in the dining room... they ran about 60 feet of 14 ga ALUMINUM wire, AND they tied it into a 50A dryer outlet, directly........
if that doesn't ring a bell, the wire was good for about 10A, aluminum wire is a fire hazard in general, and the dryer outlet was therefore capable of providing about 5x what the wire should carry..... a short in that circuit, or something connected to it would have probably caused a fire right away.
Hopefully your friend's house isn't that bad, but I'd not count on it..... When "Bubba" does wiring, it doesn't turn out good......