“They had whatted the car?”

Solution 1:

If you're going to use what as a verb in this way, you have to decline it as usual. So this is correct:

They had whatted the car?

However, while the above is certainly comprehensible and usable in speech, I would probably just say They did what to the car?

When using what as a pronoun, I prefer keeping it indeclinable:

They bought three what?

However, the plural version is also acceptable:

They bought three whats?

There's no difference of meaning between these. Some speakers may prefer one form, and some the other, but there are no firm rules or conventions about pluralization of what.

Solution 2:

It depends on which word you are replacing with what, you should usually treat what in the same way as the word that it replaces.

So, if you replace clean in They cleaned the car it would be They watted the car?, but if you replace drive in They drove the car it doesn't have a suffix so it would be They what the car?.

The idea is that the "whated" sentence should be as close to the original to be recognisable even with multiple replacements, like for example They cleaned the car into Who whatted the what?.