Welcome!

1st Question Heat: Does you temperture gauge read normal?
1.If your engine is running cold then you wont get much heat.
2. Are you sure you have enough anti freeze in the car? Low fluid will prevent it circulating through the Heater core.

2nd Question Shifting. The hard shift from Park. Could be Universal joints on the driveshaft. If you are in Neutral and shift to Drive (with your foot on the brake) do you get a small bang as it shifts? Do you get the same when you go from Drive to Reverse? Could very well be Universal joints on the Drive shaft.

3rd No start. The 13.7V..that's perfect charging voltage. No problems.
Did the car crank but not turn over or did it not Crank?
Do a Search on "Fuel pump relay" "25 amp fuse" "in-tank Fuel pump" This will help you get your feet wet on typical Volvoisms.
The intake Pump shouldn't cause a No-start unless you had less then half a tank of fuel.

Sounds scary...it isn't

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'75 Jeep CJ5 345Hp ChevyPwr and two motorcycles: it wasn't Volvossafety , it was Longevity that sold me