Learn English – Quitting a job – email subject “I’m moving on”

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.

It somewhat depends on what precisely you mean. Of your options listed, "job title" seems the most sensible and most likely to be encountered.

"Job position" is not a combination I have heard of, but you can easily guess its meaning.

"Position" is sometimes used, but I would expect it more likely to be used in conversation than on a form

Example:

"What is your position at this company"

"Post" has an older, more British or military sound to it, so probably not a good fit.

If you are asking what the person does now at their current employer, job title is good. If you want to know what they do in general for employment then profession or career might be suitable.