All four are correct. 1a and 1b mean the same thing. And 2a and 2b mean the same thing.
This question suggests exposure to a grammar book or teacher who lays out all the rules and says they're inflexible. Alas, that is not true.
First, the "rules" in those books are simply wrong. You shouldn't trust them. They
promote ignorance and mythology, like the idea that English has one single construction that is called a "conditional", instead of dozens and dozens of modal constructions, expressing various different degrees of (im)possibility, (im)probability, (un)likelihood, and (un)desirability of some eventuality, and its effects.
Second, grammatical rules are not like traffic rules in a big city; they're more like a map of the city. They lay out routes you can use, with lots of possibilities to choose from at every turn. There are also a lot of one-way streets, dead-end alleys, strange twists and turns, loops, cul-de-sacs, tunnels, subways, trains, buses, taxis, and footpaths one can take.
In the particular case, apparently there is a zombie "sequence of tenses" rule in the woodpile. This is a good example of something that isn't a grammatical rule at all, but just two different routes to the same place.
In the "a" sentences the present tense of want is used in the last clause (the one starting with whatever), and in the "b" sentences, it's the past tense. The question is which is "correct", and that seems to assume that at least one of them might not be "correct".
There are two minimally different interpretations of the "a" and "b" sentences, both of which contain the idiomatic clause whatever
X want. Both of them get to the same place in terms of meaning, by pretty much the same route.
Native speakers say both of them, and usually don't notice which one, or even that there's a difference. But when they're written, questions arise, as they always do, because writing is inflexible while speech is extremely flexible.
My favorite example of where writing gets in the way of language is how to write the negative of used to /'justu/ as in I used to like it /ay'yustu'laykət/. The problem is whether the negative should be written
- I didn't used to like it.
- I didn't use to like it.
To me, at least, both spellings look wrong, so I tend to avoid writing it, though it's certainly part of the language.