Yes they can go bad but are relatively easy to replace.
There shouldn't be just water in the expansion tank. If the coolant (50% anti-freeze and water) appears to be boiling in the expansion tank, you may have a bad head gasket or cracked head.
Water worker sounds like one of those Big Box brands. Chances are it's bad and needs replacing.
If the bladder is bad in your expansion tank the tank will fill with water. When this happens the pressure in your furnace will exceed 30lbs and your pressure relief valve will blow off.
Yes, because as the water heats it expands. The water system will then spill over to the expansion tank. The expansion tank is only big enough to store expanded water at the thermostat temperature. When your thermostat doesn't open the water will over heat/ over expand. You will see brownish burnt water marks all over the expansion tank near the overflow hole. Best off just throw away your thermostat you don't really need it.
Shut the tank down, so that it does not fire up. Was you water shut off,due to unpaid bill. Is there a break in the water line feed to the house. Did the check valve break, did someone shut off a valve to the heater. For what ever reason, if there is no water flow to the heater, it must be turned off.
Yes i would say, i can have a 30 min shower of hot water, it also depends on the size of your hot water tank.
Probably a bad heater core.
A cracked head or bad head gasket or both.
A hot water heating systems water pressure should be 12-25 psi , the air in the expansion tank should be set around 10 psi but can only be accurately tested with no water pressure against it. Usually u can tell if the tank is bad when the relief valve on the boiler starts releasing water
If electric water heater, usually bottom element going bad. Thermostat might be set too high or is going bad.
Check the heating elements in the water heater. These may be bad and need replaced.
It could be either a bad water pump or a clogged hose or a bad heater core or it could be a clogged or bad radiator.