Very minor point: No, it doesn't matter that much that there's a
vacuum, only that the pipe is partially "empty". The vacuum is just
the reason for it being empty. Although, if it were empty because of
an air leak, you would have other problems.
You problem is the check valve at the pump. Water is bleeding back
into the well thru the pump. You'll have to replace the check valve at
the pump, not the tank. Most pumps have built in check valves. Even if
your has a built in check valve, you can add another AT the pump
rather than tear the pump apart to replace the built in one. Yes,
check valves can hold and then not hold.
The check valve at the tank will hold pressure in the system if it
doesn't leak. The system can operate for years with a bad pump valve
but one at the tank. I know of no reason why one cannot be at the
tank, it is just normally not needed on a submersible pump
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