That's very likely, yes. Get it checked - a "flapping" exhauast system won't last long, but if you tend to it immediately, it may be an easy, permanent fix.
A hole in the muffler would cause a knocking sound in your muffler. A loose exhaust pipe can also cause a knocking noise.
A buildup of raw fuel in the exhaust system is then ignited and damages the exhaust muffler or blows a pipe apart.
Because of condensation the inside of your muffler, the muffler will begin to deteriorate (rust) over time from the inside. This can and will cause holes in the muffler. Along with the hole (s) the internal structure of the muffler will eventually break apart and plug the muffler, preventing the exhaust gas and the pressure from the engine from exiting the vehicle. This will cause what is called "back pressure" on the engine, causing it to lose power. Extreme example would be "you push the gas pedal to the floor but the car will not go more the 25 miles per hour". I would recommend you have you muffler replace. That should solve your problem.
A clogged muffler can.
Maybe the muffler is bad.
YES
I do not believe that your exhaust system should in any way cause your toque to become loose. Driving with your windows open would be far more likely to loosen your toque.
A bad muffler on a 96 civic could cause loud exhaust noise. The muffler could cause hard starting if it is stopped up.
Damage. Hole. Perished gasket. Incorrectly fitted. Corrosion.
Not likely. But you know you have a hole in your muffler so unless you want to have an accident from carbon monoxide poisoning you should have it replaced ASAP. Then reset the light and if it does not come back on, you know that was the cause.
A faulty muffler will not cause this but a clogged catalytic converter will.
No a bad muffler shouldn't, but a clogged catalytic converter will.