Why is 'eisiau' not used in this sentence? I don't understand where the 'wants' part comes from.
It's an idiomatic (I think that's what you'd call it) use of the preposition "am". It kind of means "for". So "I want to go to the shop" could be "Dw i am mynd i'r siop." which could be said to translate as "I am for going to the shops".
Closest similar usage in American English is "up for" as in, "Who's up for a trip to the beach?"
So could this be literally translated, "Who is it that is for passing the salt?"?
I wonder if halen is related to the "hal-" in chemical words like "halogen" and "halide", since I think those relate to salt too.
Yes, they derive from the PIE root sal- . As well e.g. Latin "sal", English "salt", German "Salz". The h as first letter of Welsh "halen" is also found in Ancient Greek "ἅλς" [hals]. (In Modern Greek "αλάτι" [alati] the spiritus asper is not pronounced any more.) The chemical words are taken from the Greek version of sal-
This switch from an original s in onset position to h is usual in Greek. (cf. "ὑπέρ" [hyper] and Latin "super"). In Welsh this occurrs also sometimes. Besides in "halen" it is in "hi" deriving from PIE *sī, English "she" (which still has the s).