94 Mustang electrical problem

My stepdaughter bought a used 94 Ford Mustang Convertible with the V-6
engine recently. The car came with a Pioneer CD player that someone else
had installed. For a few months the car seemed to run and do fine. But
for the last month or so, the car has developed electrical problems that
seem unrelated(unless anyone knows a connection).

When you turn on the stereo you get a huge surge of power through the
speakers(like a humming noise) and then it works fine after that. The
right turn signal works but blinks really fast, and both front and rear
bulbs are good(this usually only happens when one is blown, but both
work). The left turn signal works normally until you adjust the tilt
wheel all the way down as low as it will go and then the left turn signal
does not work at all. The driver's seat power controls work, but not
well(just barely work). Then when you drive the car, it sometimes will
die for no reason and won't restart for a while, but then later it will.
The floorboard on the driver's side will get really hot up by the dash
sometimes, and when you turn off the car, it instantly will cool off.

The battery connections are tight and the alternator has been recently
rebuilt. The alternator being rebuilt has made no difference to the car's
performance(it had the problems before and after, both). I told her
husband to check the battery terminals for a "good" connection, not just a
tight one. Good connection being not oxidized(he said it's not corroded
though).

Also no one has yet checked the stereo wiring to see if someone maybe done
something wrong when they hooked it up. I install stereos so I'd know, but
the car is 200 miles away from me at the moment and the stereo was already
in it when it was bought. I have done my best to describe the symptoms as
they were described to me. I hope someone here will have an answer, or at
least something to check out. Thanks.