Answers below...
* How much does Melnibonean Half Plate cost? (equipment chapter lists cost for Full Melnibonean Plate and Elric's stats include Half Plate AP and Penalty)
Half plate is breastplate and helm, so 14,000 bronze. Minimum...
* As a corollary is there a calculation for Armour Penalty and Cost for Melnib Plate/Half Plate per location?
-4% skill penalty (-2% each for helm and breastplate)
* How much arrows cost?! How much for a quiver or archer's bag?
A quiver of 10 arrows is 1 Bronze
* Are Crossbows allowed in EofM? And if so are the stats same as in Hawkmoon/RQ? Backgrounds and Skill List lists the Crossbow skill but equipment chapter does not!
Crossbows are never mentioned in any part of the Elric saga, and the fact that they crept in at all is an oversight on my part. If you want to include them, and no reason why you shouldn't if you like them and want them as part of your campaign, then use the stats given in Hawkmoon.
* What language(s) does (do) Elementals speak? Assuming High Speech myself but that is only an assumption.
They'll have their own tongue, of course, but Hi Speech is a good assumption.
* How do Elemental Hit Points work? Are we talking 1 Location with all Hit Points?
Yes. 1 location with all the hit points.
* Why are base chances for Elementals (and presumably Demons) so different from Humans?
Because they're NOT human...

. In general, elementals only have access to the skills listed. If you feel an elemental needs, or might have, another skill, then use the same calculation as for a human character - if the elemental has the requisite characteristics (sylphs, for instance, donj't have CON, so they require a different calculation). Same goes for demons.
* A couple of cults talk about granting a 'Rune' are these Runes a la MRQ RuneQuest Runes? And if so which Cults get which Runes? Or are they more like the Runes and Spheres from Unknown East?
Runes are very different to the standard MRQ runes. Rune magic is fully covered in 'Magic of the Young Kingdoms' but was originally part of the main rules and was removed for space reasons. I tried to catch all references to runes and remove them but, like crossbows, a few slipped through! If you're not using 'MoYK' then ignore runes for now, but you can add them in when/if you get that book. But they are powerful and designed specifically to cover the effects of the magic found in the saga and, yes, do reflect the kinds of properties found in 'The Unknown East' magic system.
Hope this covers everything for you!