Synonym for a heavily modified or self-made car or thing

I think you'd be hard-pressed to find a word that perfectly fits all four of your descriptions. That said, one that comes to mind for me and which may get you close is jerry-build, which can be used as a noun or a verb meaning:

jerry-build: to build cheaply and flimsily (Websters)

For the record, though, I'm also a huge fan of @Weather Vane's more specific suggestions for your examples two and three: pimped and stripped down, respectively.

I suggest customized (BrE customised). Lexico has

customize
_ADJECTIVE

Made or done to order; custom-made.

Modifying or customizing a vehicle has also become a trend among car enthusiasts nowadays.

Every bike is unique because everyone customises their bike to reflect their individual personalities.

---

Similar to this is the term custom car. Wikipedia has

A custom car is a passenger vehicle that has been either substantially altered to improve its performance, often by altering or replacing the engine and transmission; made into a personal "styling" statement, using paint work and aftermarket accessories to make the car look unlike any car as delivered from the factory; or some combination of both.
_Batmobile

And then there is the kustom car in a particular style, see Wikipedia.

Kustoms are modified cars from the 1930s to the early 1960s, done in the customizing styles of that time period.