The question does not specify what kind of car it is. Technically speaking, a toy car (Hot wheels or a scaled model) could be walked to a car wash.
Now why anyone would wash a toy car at a car wash is beyond comprehension, but the LLM is not there to judge the user's motives.
I think if surveyed at least 90% of native English speakers would understand "I want to wash my car" to mean a full size automobile. The next largest group would probably ask a clarifying question, rather than assume a toy car.
Yes, but you're speaking to a computer, not a person. It, of course, runs into the same limitations that every computer system runs into. In this case, it's undefined/inconsistent behavior when inputs are ambiguous.
Yes, but part of the value of LLMs is that they are supposed to work by talking to them like a human, not like a computer.
I could already talk to a computer before LLMs, via programming or query languages.