Bad? Well you do use more fuel and put more strain on the drivetrain, but I would not call it bad.
yes, you are causing it to run richer.
Check the fuel filter or the fuel pump.
Because it's broken.
Only when accelerating, I would suspect a broken motor mount or bad CV joint.
speedy; accelerating; flashing; fleeting; quick; rapid
Possibly bad fuel filter
you have a bad fuel pump
Bad ground or alternator stating to go bad.
Bad ignition coil
acceleration is a measurement of increased speed change (deceleration being that of decreased speed change). your current speed (Whether fast, or slow) is irrelevant, as long as it changes, and increases, which means you are accelerating.
Loss of power when accelerating can be caused by a number of things. A leak in the fuel line or even a bad alternator can cause this.
Could be a universal joint gone bad.