Do ghouls need to eat and drink to survive?

Solution 1:

Yes, but sometimes Bethesda forget or ignore this. This also applies to super mutants and even humans.

For purposes of this answer, I'll also cover super mutants.

In the non-Bethesda games, every post-human has some explanation for where they get food and water. Harland (actually in New Vegas) mentions radroaches and condensation. Dean uses the Villa's vending machines. Jacobstown has a small garden and a brahmin herd (and Marcus complains about the NCR killing those brahmin). It's clear that they need food, even if their immunity to radiation, disease, and poison makes them a lot less picky.

Cases where they survive with no supplies are found in Bethesda games. Peabody and Fawkes, for example, apparently survive without food for several years.

Megaton also has no visible food supply, besides apparently scavenging a 200 year old super market filled with raiders, who apparently don't eat anything either. Shamus Young does this rant better than I ever could.

There is no case in a Fallout game where the player asks a post-human what they eat, and is told that they don't need to. If they apparently don't, it's an oversight, not something specific to ghouls.