I found the problem. The problem is with the wheels on the YFT models. All the other vehicles that have working customization and tuning do not have the rear wheels in the YFT models. This one and the Beck Customs F132 have the rear wheels installed on the YFT model. I think what I need to do to fix this is get Zmodeler or something that can make YFT files and delete the rear wheels.

I noticed that the wheels are colored by the secondary color option and not the wheel color options. Maybe this is related to the wheel coloring. There's another mod called the Beck Custom F132 that has this issue - secondary color wheels.

@krashadam and that would make all the other parts invisible? To where and what do I type in to register the wheels?

I was trying to turn the Comet 6STR (https://www.gta5-mods.com/vehicles/pfister-ruff-weld-comet-widebody-tuners-and-outlaws#comments_tab) into an addon, and I've finally managed to get the game to recognize the parts. My problem is that the parts are not visible but are still listed. Even the wheels don't change no matter what wheel I select.

No, this is not the same error that most people complain about - having no tuning options for a vehicle. I have a unique ID value for my addon so don't refer me to a list of ID numbers. Now, I am accepting of the idea that the problems are similar in nature, but they are not the same exact thing.

I've also noticed that the force fields for things like the spoiler are still recognized when I stand on it even though the spoiler cannot be seen.

Oh, the problem is OpenIV, not Scripthook. The cars that it removes are: the Verlierer, the Cognoscenti, the Cognoscenti (Armored), the Cognoscenti 55, the Cognoscenti 55 (Armored), the Schafter LWB, the Schafter LWB (Armored), the Schafter V12, and the Schafter V12 (Armored).

Alright, the mods installed through Scripthook won't work. I'm going to try replaced the mod's x64e.rpf with the game's original one.

PROBLEM SOLVED!
The mods folder was corrupt. Just remove the mods folder. My mods still work, but I don't know how they still work without a mods folder. I was looking at other "invalid errors" for modded vehicles, and the solutions all seemed to pertain to the mods folder. Here's a more in-depth look if you wish to keep your mods folder. forums.gta5-mods.com/topic/7354/add-on-cars-invalid

I reinstalled the game, and I still have the same problem.

To be specific, the missing vehicles are the variants of the Schafter and the Cognoscenti (The Coupe hardtop convertible still works). I was installing some basic mods such as the single player apartments mod and the Benny's singleplayer mod. When I checked Menyoo, it wouldn't let me spawn my personal saved versions of these vehicle, and when I checked the Sedans list, they were missing entirely. I haven't dabbled with modded vehicle addons/replacements. I was wondering if there is a way to restore the files for the vehicles without uninstalling the game. Also are there any known mods that create these conflicts which seem to delete default cars? Yes, these vehicles were working with Menyoo when it was just simply Menyoo.

Mods used:
https://www.gta5-mods.com/scripts/single-player-apartment-spg-net
https://www.gta5-mods.com/scripts/enhancement-script-for-per_zeus-raindrop-texture-mod
https://www.gta5-mods.com/scripts/benny-s-motorworks-sp
Menyoo and all the other stuff that I have to install in order to run mods.