After a time playing, the cars lose the exterior of the chasis

This is caused by SkyRe, it makes the ghosts invulnerable when you are not attacking them. That the fake destruction spell can damage them sounds like a bug to me. Might want to mention it to the creator of skyre.

You can read more about the changes Skyre makes in the skyre guide. Ignore the silly description of the mod, the guide is actually pretty clear in what skyre changes.

Have you tried turning it off and on again?

One important note on disabling mods in skyrim. Skyrim is not oblivion or fallout. Mods are hard to disable on a running game. Any scripts that a mod includes and attaches to objects is saved inside the savefile. So in a lot of cases disabling the mods has little effect. (At least not until the objects respawn).

It is very easy to bloat and eventually wreck your savefile by installing and then disabling mods. When using new major mods, always use a clean safe, or, a clean game start.

There are a few 'tricks' you can use to more safely disable mods. First, if you are using SKSE, you can create a SKSE.ini file in the "my documents/skyrim/SKSE/" directory. (location of this dir may vary, it is the same one as the skyrim.ini dir). Add the following line to the ini file:

[General]
ClearInvalidRegistrations=1

This should remove invalid scripts.

And always follow this guide when installing new mods.

Apparently, the reason for losing Stamina constantly wasn't a mod conflict or anything, it was my own stupidity. I didn't know that wearing Heavy armor in Requiem caused a Stamina drain if you did not spend any perks on it. I was wearing a Heavy helmet. Removing that got rid of the Stamina drain and it's all good now!