First issue seems backwards, under load(climbing hills) engine generates more heat.
Heater getting cold is either because engine was cold or there was an air bubble blocking flow thru heater.
I don't think Mountain driving's outside temp could lower engine temp that much, but the Lima(2.x) engines were known to run very cold in cold weather.
You need to test alternator after battery has recharged from starting.
First with engine off get battery voltage, should be 12.4 to 12.8vDC
Battery voltage should now be above 14vDC, that is the voltage regulator recharging the battery from starting.
Wait a few minutes and voltage should drop to 1 volt above battery voltage, so if battery was 12.5vDC then you should see 13.5vDC now.
This is the voltage regulator maintaining the batteries charge.
If voltage stays above 14vDC then battery will be ruined.
Now once battery voltage is down to 13.5-13.7vDC turn on the lights, the fan blower, leave door open, basically turn on everything you can think of that is electric.
Voltage should drop and then come back up to 13.5vDC as voltage regulator turns up up the output of the alternator.
If voltage gets down to 13.0-13.2vDC then one of the fields in the alternator is bad(or a set of diodes for that field is bad.
Alternators generate AC volts in 3 fields, each field goes thru a set of diodes to produce DC voltage.
Most common failure of an alternator is a field failing, it often goes unnoticed until a second field fails, this is because the alternator can still charge and maintain battery at high RPMs.
The dimming of the head lights at normal idle(750-800rpms) is a sign of a failed field.
No it is not normal, lol, as some will tell you, no car/truck maker would install an alternator that can't produce enough voltage at idle to operate the system.
Now if you add subwoofer amps or other larger power draws then dimming head light my be normal at idle, but not with stock system.