Water heater backflow preventer valve failuer

my advice, remove the backflow preventer, it's part of the cheaper water heater bypass with only one quarter turn valve. remove the valve, install the two valve water heater bypass.

the check valve really isn't needed for anything else.

Why remove it?

well, the check valve flow is nonlinear with pressure, so what we, and others have found, is that when you get the water temp right for say a shower, then turn the flow down, water temp changes, usually cold.

The RV dealer we bought our trailer from says they have more trouble with the check valves than anything on the water heater.

When dealing with water and dissimilar metals galvanic corrosion is the issue. Stainless, brass, & aluminum are indeed dissimilar in this regard. Aluminum tanks should not have an abode rod because the rod will reverse rolls & instead take molecules from the tank vs giving molecules to the tank. The tank and fittings being discussed should give many years of service regardless of the fitting locations.
Many installations omit the check valve but if present it should be in the outlet so expansion/contraction can occur via the cold side especially with an accumulator present.
Plumbers putty? I would expect to see joint compound our Teflon tape. Putty will not hold pressure & is applicable for drain baskets and casual water intrusion situations. If indeed it is thread compound it should assist in disassembly. As others have stated any proper sized check valve should work or you may opt to eliminate it. There must be a valve on the tank side of the bypass to prevent antifreeze from entering the tank when winterizing.

What is make of WH?
If tank is aluminum, then it is an Atwood and no anode is used.
You maybe able to flush the spring out through the anode or drain plug. Fill water heater then remove drain plug or anode.
No a big deal to leave in tank.
Aluminum and brass should not seize. My guess it is just tight. If there is something to grab hold of, apply more pressure. If nothing to grab hold of, you will need to get an easy out to remove broken portion.

My w/h do not have such valves, but if it is a spring that come off the valve that is in your tank, I don't think you need to worry about chemical reaction.
The spring has to be Stainless steel and that is neutral to about everything. Long-term mechanical damage might be an issue.
Bras and aluminium should not corrode neither.
Can you post a picture?

The spring will be made out of stainless steel. So it wont hurt anything if it's in the tank.
As for repair, if it looks bothersome to replace then I would just use a separate shark Bite fitting and add the CV to the line.