Niall is correct. Opening the T&P valve to drain water from the water heater is a common practice, but if it's really old, it can be damaged by sediment and corrosion. Where the plumber went wrong is not using the T&P valve to drain some water, but rather trying to hammer it shut. T&P valves prevent BLEVEs (Boiling Liquid Expanding Vapor Explosion), which are a type of catastrophic explosion -- in this case, in the event of a malfunction in the water heater. Let's just say that if your water heater BLEVEs, you can kiss your entire house goodbye, so since there is clearly a problem with your T&P valve, you need to get yourself a new one.
In order to replace the T&P valve, you can call a plumber or do the following:
1) Turn off the cold water ball valve.
2) TURN OFF THE WATER HEATER'S BREAKER IN YOUR BREAKER BOX (if the top heating element hits air, you can damage it, and it will make a massive shotgun-like sound)
3) Open some hot water outlets, such as the hot water handles on a few sinks. These will allow air into the top of the hot water heater.
4) Run a garden hose from the hot water heater's drain to the street/driveway.
5) Open the water heater's drain, and empty the hot water heater below the T&P valve.
6) If it does not flow on its own, you have sediment build-up (which you most likely do if your T&P is failing.) If it doesn't flow, open the cold water ball valve so that the water pressure can help break through the sediment layer. After 2-3 minutes, close the cold water ball valve again to allow the top of the water heater to fill up with air.
7) Replace the T&P valve. Use teflon tape to help create a seal.
8) Turn off the drain.
9) Remove the garden hose, but keep it held high so no water comes out the end that is in your hand... and take it back outside.
10) Open the cold water ball valve.
11) A mixture of water/air should come out of the still-opened sinks after 1-2 minutes. You can shut them off at this point if you don't mind seeing the air bubbles the next time you use the sink.
12) Turn the water heater's breaker back on.
I have a setup similar to yours and the radon installers put a foam sheet over a hole in my sump cover, almost like a thin sheet of packing foam. This is almost airtight but allows some suction for the fan. You could terminate the drain line over a small hole that was covered with foam or paper such that the the air would be sealed in, but in the case you get water from the heater it would drip through it. You could also put a check valve in the pvc line from the heater but it would have to be loose so a trickle of water would trigger it. A trap would dry out, although the HVAC trap probably dries out during the winter anyway....but the suction from the fan should override that small opening.
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The drip pan's drain tube may not be large enough to handle the flow if you drain the entire water heater through it, leading to an overflow of the drip pan. I would be safe and use a hose to connect the outlet to the drain.