#1
does it hurt your truss rod if u keep your guitar in drop c or lower for a long period of timei personally believe it does
#2
I would believe that it would actually relieve pressure on the neck if the guitar is detuned. A luthier once told me that a standard tuned guitar has I believe 40 pounds of pressure on each string.
#3
not if you get your guitar set up for that. If you switch from standard tuning and leave it there for a while, I am sure its bad.
top axes:
Taylor GS8
Fender American Strat (w/DiMarzio pickups)
Epiphone Les Paul