If you want to ask a favour, you use the wnei di form. So Wnei di yrru'r car? is like saying "Will you / Would you mind / Could you drive the car?". Fyddi di'n gyrru'r car is just an enquiry about the future, "Will you be driving the car?". You could think of the Wnei di... form as a polite command almost.
Careful with the answers too:
Wnei di yrru'r car? / Gyrra'r car! answer: Gwna(f) (i) / Na wna(f) (i)
Fyddi di'n gyrru'r car? answer: Bydda(f) / Na fydda(f)
They're not always interchangeable.
- "I will be" = bod
Bydda i 'na "I'll be there"
Bydd hi'n oer "It'll be cold"
- Asking a favour or making an offer = gwneud
Wnei di ddod hefyd? "Will you (please) come too?"
Gwna i heplu "I'll help" (as in, you're offering to help)
The bod forms just ask for information.
Fyddi di'n dod hefyd? "Will you be coming too?"
Bydda i'n helpu "I'll be helping"
- Determination, immediacy = gwneud
Gwna i weithio arno fe heno "I'll work on it tonight"
Bydda i'n gweithio arno fe heno "I'll work/be working on it tonight"
The first sounds a bit more determined.
Gwna i dalu "I'll pay"
Bydda i'n talu "I'll pay/be paying"
The first has more immediacy, more reference to the near future.
- Otherwise they seem to be interchangeable.
Gwnaiff / Gwneith hi fwrw fory / Bydd hi'n bwrw fory "It'll rain tomorrow"