You can close the isolation valve going to the house if you want. The drain on the tank is as good a ”faucet” as any of them to drain the tank. With the pressure tank drained, the house is effectively at zero pressure as well, so it really doesn’t make much difference.
Yes leave the drain faucet open while adding air to the tank. If air comes out the drain faucet, the bladder is bad. Higher than normal air pressure in the tank usually means the bladder is busted as well.
A 44 gallon tank holds about 12 gallons of water as well. So you can measure this in a bucket as the pressure drops from 60 to 40. With the correct air charge, if you are not getting close to 12 gallons out of the tank, something is wrong with it.
It doesn’t matter how old the pressure switch is. If the pump still comes on at 40 and off at 60, the pressure switch is OK.
If everything checks OK, and the only time you get a short cycle is when back-flushing, there could possibly be some restriction in your flush line.
Your use of Bold actually helps in this case.