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The drink parallel of famished is parched.

parch
_{Dictionary.com main section}
5. verb (used without object) to suffer from heat, thirst, or need of water.
_{Dictionary.com "World English Dictionary" section}
2. (tr; usually passive) to make very thirsty: I was parched after the run

Dehydrated is a more clinical term, and would be parallel to malnourished, I think.

Both famished and parched can be used in both formal and informal contexts, although they're frequently used with a bit of hyperbole implied, which skews them toward the informal.

I'm so parched I think I could drink a river.

There are also a lot of idioms out there to signify extreme thirst, such as the "spitting cotton" one mentioned by CopperKettle, but if you're looking for the most straightforward parallel to famished, then you really can't do better than parched.

1) and 3) are OK and sound fine. I won't comment on whether wide or big is better, as that would depend on the subject and opinion of the writer. Though I think big would probably be used more often.

2) I would use bug-eyed, though this has a negative connotation and could be insulting. In any case, I can't see that any term describing such a condition would be taken positively.

4) He is very wide-mouthed.

This seems like you are describing him or his behavior, rather than his mouth. Something like:

He is very open-mouthed (talkative).

But I doubt you would normally hear a phrase like 4).