The expansion tank neck is bonded to the main part of the tank. The bonds have been known to fail resulting in the separation of the neck from the rest of the tank and the loss of of the ability to run the cooling system above atmospheric pressure. If the picture is your new tank (as in new to you) I might be inclined to actually order a true new tank
Expansion tank Amazon/140/1800 | Cooling system 142 B20 1969-74 (vp-autoparts.com)
Your new / old tank may just be waiting to fail in the same manner. If you are going to attempt to repair the old tank epoxy would not be my choice. I would look for an appropriate solvent cement. However, given that new tanks are available I would only use a repaired tank as a temporary fix.
First question - On my B20 if I am driving around in temperatures of 20 C or less on level surfaces, lack of pressurization of the cooling system will not result in overheating. If am zooming about and quickly climbing steep hills lack of pressurization could lead to boiling, then loss of coolant and then overheating. My observation about not over-heating assumes that your radiator is in good condition and that you are running a proper coolant mix (not straight water). Coolant mixes actually have a boiling point that is higher than the boiling point of water so you may encounter 'boiling ' with water where a coolant mix will not boil.
If you climbed some really long steep hills and your radiator is in poor condition and you are running straight water, I can see that loss of pressurization could lead to boiling and significant coolant loss and subsequent overheating.
Second question - no / yes. If the tank in in good condition, the pressure release cap on the top of the expansion tank will release pressure (and vent coolant) if the pressure exceeds the rated operating pressure of the system. This should prevent failure of the tank neck. If the tank is in really poor condition then the bond may fail at a pressure below the operating pressure of the release cap. I have seen people stick sealed caps on the expansion tank (no pressure relief feature) which can result in over pressurization of the cooling system and tank (and other) failures. If the pressure cap has the wrong rating (too high) this can lead to failure.
How did you test the thermostat? My experience has been that if you have a significant overheating event the style of thermostat that Volvo uses tends to fail open. Finding a bone dry thermostat would qualify as significant overheating. Did you do a boiling water test and confirmed that the thermostat is going open and closed? The B18/20 uses a thermostat that has a valve on the bottom that closes off an internal coolant by-pass in the engine.
Thermostat B18/B20 (71°C, 160°F) | Cooling system water andFan (vp-autoparts.com)
Make sure that you have the correct thermostat with this valve. A lot of the aftermarket thermostats sold for the B18/20 will fit; but, lack this lower valve which leaves the by pass open which means that all the coolant is not getting forced through the radiator.
Third question - I don't know about failure of the 122 capillary tube temperature gauge. If you are uncertain about the temperature gauge, any electric temperature gauge should work provided you can get the correct correct adapter to fit the typical 1/8 NPT temperature sensor into the sensor hole at the back of the head. The adapters are out there - I have one on my B20E. Rustinmotion's idea of getting an adapter to fit in the top rad hose and putting the electric sensor there is a good idea.
Without knowing what you have done to the heater circuit it is impossible to give you a definitive answer on flushing. When the heater valve is closed coolant flow is blocked in that circuit so you still should be able to flush the engine and rad. However, two problems. The old crud trapped in the heater circuit will eventually make its way into and contaminate your fresh new coolant. The even bigger problem is that air may get trapped in the heater circuit during the flush which does not get bled out and eventually works its way into the main cooling system causing grief. If you have run a hose from the outlet on the back of the head to the return pipe going to the pump which completely by-passes the heater then flush away with impunity!
Given the age of the car, unless you know that this has already been done I would remove the rad from the car and take it to a cooling system specialist and have them hot tank / pressure clean / de tank and rod / whatever the rad. Dumping a bottle of cooling system cleaner into the cooling system and running it around for a few minutes is not going to fix s severely plugged radiator.
Rustinmotion's idea of a reagent test on the coolant is a good idea. You don't need to go to a garage to do this. You can purchase the test kits and do it yourself if you want.