Yes, the computer is the voltage regulator.
Most likely cause is a leak. Could be a shock or a line.
Yes, that is one of many possible causes.
A raidator in need of a flush will not cause a battery drain.
alternator or bad wires
If no light is on and no relay is stuck then the battery has a dead cell and needs replacing.
You shorted it out, try protecting the wire ends from touching anything metal next time. the wire ends on the battery?
There could be various reason why the display could show but no readings appear on a 1988 Chrysler New Yorker. A faulty sensor can cause this issue. A scanner can help diagnose any faults that may be in place.
Bad master cylinder.
A likely cause is an internally restricted radiator.
Battery size is measure in 2 ways. The actual physical dimensions of the battery and the size in Cold Cranking Amps (CCA). Purchase a battery that is physically the same size as the battery you are replacing or it will not fit. You can purchase a battery with a higher CCA capacity than the one you are replacing. This will cause no problems at all, and will just be a better battery, especially in the winter.