I recently purchased a home and noticed that the following wiring method was used connecting the 240 volt circuits. The branch circuit distribution panel has 4 wires serving it, 2 hot, 1 neutral and 1 bare stranded ground and a solid copper ground wire grounded the copper plumbing. The branch circuit distribution panel is not bonded as the main breaker is located on the outside and bonded there.
Water heater #1 is wired with 2 hot wires (red and black) to a 30 amp double pole breaker and the white wire is tied into the unbonded neutral terminal on the panel.
Water heater #2 is also on a 30 amp double pole breaker with a red and black hot wire and the white wire is located on the ground terminal. Isn't one of these 2 methods improper? If the panel was bonded the answer would be no but since it isn't bonded doesn't it matter? I am thinking it does matter and the white wire tied into the neutral terminal should be located on the ground terminal. Am I correct? If not please explain. I also have a heat pump condenser located on a 50 Amp breaker using 2 insullated hot wires and one bare ground wire. The bare ground wire has been placed on the neutral terminal. This all seems wrong to me. Doesn't 240 volt equipment have 2 hots and an equipment ground and no neutral per say? On a panel that isn't bonded isn't it important to keep the ground and neutral separate?
The 50 amp dp breaker for the range has 2 hot wires and the bare ground wire is connected to the ground terminal.
The clothes dryer is located on a 30 Amp DP breaker and has 10-2 w/ground. The ground wire is attached to the ground terminal.
The air handler has a 100 amp DP breaker with 2 hot wires and one insullated wire connected to the ground lug next to the incoming ground on the distribution panel with the bare ground wire cut and not connected to anything. There is an FPE subpanel mounted on the air handler. The subpanel is a FPE stab lok breaker panel and has both hot wires connected to the bus and the shielded ground wire attached to the neutral terminal that is is unbound. The FPE panel with stab lok breakers has inherent issues I am aware of but it has one 50 amp tandem breaker feeding part of the air handler and another 60 amp dp breaker also servicing the air handler. I am assuming that the 50 amp leads service one of the two electrical heating elements and the other 60 Amp leads service the blower, electronics and the other heating element. Isn't this tandem breaker not allowed on such a configuration? It has thrown several times but the secondary breaker located on the air handler in another area doesn't throw. I am going to replace the FPE sub with a new Square D sub and want to know it it would be best to use the cut bare ground wire at the distribution panel as an additional ground wire to the sub panel's ground terminal. The air handler is getting old and going to be needing replacement soon and I am also trying to bring the wiring up to par for a new system. It is my understanding that a lot of newer 240v appliances (range and dryers) and are now using 4 wire instead of 3, are air handler w/ electric resistance heat also being changed to 4 wires?
The branch circuit distribution panel appears to have been replaced at some point in the past as there are quite a few splices within the panel and the inspection sticker on the exterior main reads 1993 so I am guessing the panel was replaced on that date. I know that is a lot to put into one question but some help would be appreciated. Can provide photos if needed for clarification. The branch circuit distribution panel is a mess and so bad not sure if someone would be able to follow a photo of it any way!

Water heaters are usually straight 240 volt and do not need a neutral.
Water heater # white wire is probably the ground and should be connected to the ground bar, not neutral bar.

Need to learn what the air handler and heating systems requires, 240 volt or 120/240 volt. This will determine if a neutral is needed. Bare grounds should be connected to a ground bar.

Photos are always welcome, even if for entertainment, and illustration of poor workmanship.

Well in this circumstance it would certainly be entertaining and a perfect example of poor workmanship.
I had a feeling that water heater #1 should have terminated the white wire on the ground terminal instead of the neutral terminal, but wanted a professional opinion.

The HP condenser has a disconnect and 240v entering it but not sure how that is broken down once inside the unit. It is a Trane XL1000 Weathertron 3 ton unit and slightly undersized for the home. It should have been a 3.5 ton or 4 ton unit. The home is 1850 sq ft above grade with a partial basement of approx 1600 sq ft all finished with 4 supplies and 4 returns. This is the circuit that has a bare wire from the distribution panel connected to the neutral termnal and 2 hot wires leading from a 50 amp breaker. The HP needs servicing as the suction line is cool and the liquid line is warm during the heating season and blows nothing but cold air. May be a reversing valve or solenoid, my best guess. Still thinking that the bare wire should be on the ground terminal instead of the neutral terminal, but again wanted a professional opinion.

The airhandler houses at least 2-5kw heating elements. No BTU ratings on the air handler so I am guessing at the number of elements based on the breakers alone. 1-50 amp dp breaker and 1-60 Amp dp breaker and 1 20 Amp breaker installed in the subpanel mounted on the air handler. The 20 amp breaker serves the electronic air filter that doesn't work. The air handler is an older GE unit from the mid to late 70's and appears to be the original one to the home based on that age. The model is GE Mod# BWE9360G100D0. It may need a new contactor since it has a bit of a humming sound to it, but so far it works OK. At the distribution panel it has 1-100 amp breaker with 2 hot wires leading from the breaker and 1 insullated conductor connecting to the ground terminal and a bare ground wire cut back and unused. This is what leads to the subpanel on the air handler noted above.