Gearing up for first EX raid

1. Lick is better because of its DPS, which matters most for fast moves for raids. Hex might deal twice the damage per hit, but has lower DPS.

2. You can only guess the quick move by looking at the animation or damage it deals.

3. I remember Weavile being the best, but I have not looked at damage calculations myself lately.

All in all, Deoxys attack is so weak that you don't need to optimize much if you battle with 2-3 additional trainers. Level 40s can solo it.

Assuming you're not planning to solo, you don't need to invest anything. Three dark Ttar will be more than enough.

For reference, I just did mine yesterday:
My girlfriend was in a group of 20 and she killed it in about 8 seconds (12 including the 4 to load in).

I did it in a group of 5 (two of which were level 25-29). We killed it pretty quickly too. It one shot my gengar with its first charge move (after I got a shadow ball off) and then nearly one shot my mewtwo with a dark pulse as well (level 40 91% barely survived the charge attack, which let me get off an extra Shadow ball). Then ttar came out and survived 2 charge attacks and we killed it as the 5th total came off.

So if you have a group of 5+, you won't even need the third Ttar.

Now to answer your other questions anyways (although I recommend not powering up anything extra for this):
Lick gengar is better because lick charges energy faster for Shadow ball (and also casts faster than hex). So while hex does way more damage than lick per cast, you can use more licks AND have more energy sooner to use Shadow ball (with hex you might not even get that first Shadow ball off before dying to the raid boss charge move). In general I wouldn't recommend gengar for this: he was pretty good for Mewtwo and excellent for Cresselia - but completely unnecessary for deoxys attack. When deoxys defense rolls around, it'll probably be very worthwhile though.

I'd assume weavile is the best of your listed dark attackers.

I've solo'd 2 atk deoxys, its extremely easy.

Feint attack weavile over honchkrow and houndoom, always. Tyranitar is also a great option, in my opinion the best option, having DPS slightly under Weavile's but the much better defensive stats and typing allowing it to outperform weavile (as in a team of only tyranitar and only weavile, from what ive heard, the tyranitar do better due to not fainting out as often)

A single hex v a single lick will turn out in hex' favor, however, hex is a slower move than Lick. Lick has very similar EPS to hex (meaning they get charge moves at a similar rate) however lick has significantly more DPS than hex. The base power of a single move from hex might be stronger, but cooldown of the moves also is important, which is why lick preforms better.

You are able to tell when fast move Deoxys has, but you need to pay close attention to it.
The game never outright states what fast moves bosses have, so you need to pay attention for yourself. If you dont see the very distinctive animation of zennhead butt (that circle thing that appears when attacking, very recognizable if you fight blissey or metagross regularly) then its poison jab, if you do see the circle thing, its zenheadbutt. Ive never found either one particularly harder, mostly because I just lead my tyranitar and they resist both of those moves, if using gengar it is more important to know.

1. Yes, you are reading that correctly. Hex technically does twice as much damage, but Lick is better because it has massive energy gains and is crazy fast, allowing Gengar to use more Shadow Ball before it faints. Therefore, although Hex does more damage, Lick is better for glass cannons like Gengar that need moves with fast energy gain.

2. That can be solved with using the "recommended" feature. I use it all the time. If you want to use parties instead, consider these:
- Poison Jab can be a neutral threat, but consider that TTar and Gengar both resist it, where almost everything else takes neutral to it.
- Zen Headbutt would be a better move for TTar to go up against, but Gengar would take SE.

3. By a wide margin, use Feint Attack + Foul Play Weavile if you have it. It's the best Dark-DPS out there. If you have Snarl + Foul Play or Crunch Houndoom or Snarl + Dark Pulse Honchkrow, they are perfectly usable and, actually, great options, but Weavile with a full Dark set is better than both. THEN AGAIN, you have 3 Dark TTar's, which perform a bit better TDO-wise due to better bulk, while still producing very good DPS. Weavile is more of a glass cannon, but it does more DPS.

1. You are reading it wrong. That's the power of the moves, Hex does twice as much damage per use but is more than twice as slow. Lick has better DPS.

2. You can sometimes deduce the fast move as well but it's much more difficult.

3. Don't invest anything into anything unless you want to solo it and think your team isn't up for the job. Weavile is by far the best dark attacker out of the three.

The question whether the fast move is better with high DPS or high EPS has a HUGE element of random chance with the attack forme of Deoxys. The reason is that most attackers invariably feint from the first charge attack of this boss. The question on e.g. Shadow Claw - Lick - Hex on Gengar depends entirely on whether you will be able to fire an extra Shadow Ball. Which is just a matter of luck in this case.