As a general rule of thumb: Praying to any given god increases favor for that god, increases favor for the gods just above and below alignment wise a little less, increases favor for the gods one past that a lot less, does nothing for the gods one past THAT, and knocks your favor with all the rest. For example:

I pray to Loricatus (N=). I gain, say, 10 favor with him (these numbers are coming straight out of my ass, btw). I also gain 6 favor with Silva (N+) and Mellis (N-), and 3 favor with Sophos (L-) and Cleptia (C+). Nothing happens to my favor with Seges, Dulcis (both L), Nefas, or Scabies (both C). I lose favor with all the rest of the gods.

Now I may be wrong on the range here; praying to a god may only increase for one alignment range, do nothing, for two, and cost you for the rest. But I think that's about right. I know it's reasonably viable to pray to up to a 5 alignment range worth of gods, as long as you do them all at the same time and are careful not to anger any of them.

That's another thing, this is all assuming your prayer doesn't result in an anger effect. I have no idea how that would influence favor.

You can't

EDIT: Well, not entirely true. You can't can foods, though praying to Mellis can fill up to 5 empty cans with random foodstuffs. However you can also zap rottable items with a wand of slow, which causes them to rot much more slowly. (You can also zap them with a wand of haste, if you want them to rot away really fast.)

Atavus' arcanite plate mail is actually available starting at only 500 piety. Higher piety increases the likelyhood that he'll give it to you when you pray though.

You have to get 1000 (I believe) piety points with a god to become their champion; however, this only matters with Mortifer and Valpurus, as they will hurt you if you pray to them without being their champion.

As far as when to pray, you should do it roughly once every 3 game-hours. To make it safe you may want to go a little longer, do it once every 4. Praying never makes you lose piety unless you get a negative god effect, in which case the prayer time-out counter is a LOT longer. Also, praying early will cost you piety and will give you a long prayer timeout. I'm not sure exactly how long but I'd advice waiting a day or two before praying again in either case.

As far as alignment... I'm not sure. It's certainly tied to which gods you pray/sacrifice to, I'm not sure if anything else contributes to it. I don't know about it's ingame effects. Certain weapons will also draw your alignment towards chaotic -- Neerc se'Ulb, and I believe Mjolak. This will have an adverse effect on your standing with lawful gods.

This may be true but I don't know of very many people who've actually killed Sherarax and Ischaldirh. Also if you don't know the Enner is not randomly generated.

'A'pply a pick-axe on the walls.

Yes, scrolls of repair fix limbs. The horn of terror makes monsters nearby run away.

Wisdom helps you with god relations -- you gain more favor when you pray. With enough wisdom it's possible to pray to Valpurus and gain favor with Mortifer. Raising it can be hard -- I believe it can be sci-trained, the only other methods I know of are reading holy books, prayer, and sacrifices.

As for bones files (when you find a corpse of yourself), they happen on levels you died on. However certain game features being disturbed -- such as Jenny, the secret rooms in the GC, the Enner Beast, the shop -- will prevent bones files from generating in the first place.

And on the wands -- A wand of necromancy will make a rotting zombie out of a corpse. A wand of resurection actually brings them back to life. However, the wands of resurrection only bring the body back to life -- if there is no soul nearby to inhabit the body, it'll die again immediately.

This is super-minor but would it be possible for there to be a way to change your poll votes?