If you're measuring 11 volts at the battery, your alternator isn't producing any charging current at all. It also means your battery is pretty heavily discharged:
(all voltages are measured with the engine off, after the battery has been setting for a while)
When the engine is running, a good alternator will keep the battery at around 14 volts at idle (assuming no no huge power-drawing electrical accessories are turned on), or a solid 13.5 volts with your headlamp high beams on.
Often, a bad alternator will make a whining sound that can be easily mistaken for engine or transmission noise.
Low battery voltage causes all kinds of dashboard indicator light problems, engine and transmission driveability problems, etc.
So, you should probably fix the alternator before attempting to diagnose any other problems you're noticing. If you're lucky, your other problems will disappear afterwards.