Yes, it can work. You would probably need 8 Incubi and two Haemonculi in two Venoms. Biggest problem will assault grenades because you will attack at initiative 1 without them.
If you are looking to use your warriors for long range anti-infantry support, it's hard to go wrong with Venoms. You have 20 Warriors so you should be able to make 4 Blasters (2 actual blasters and two converted from Shredders and Blast Pistols).
1)For anti-tank, the general consensus is that Ravagers, 3-4 Kabalite Trueborn with Blasters in a Venom being optimal, although a Razorwing Jetfighter can also be used to hit bubble-wrapped armor. Raiders and Reaver Jetbikes are also viable, the former coming with Dark Lances stock and the latter being able to take Heat Lances/Blasters. Having suicide Wyche squads with Haywire Grenades in Venoms are also good.
On a side note: I find myself preferring a mixture of Raiders and Venoms as opposed to just Venoms. While you lose long range anti-infantry, you gain more long range anti-tank and fairly brutal mid-short range firepower with Splinter Racks. That's just an opinion though.
2)Given the stupid amount of Anti-Infantry Dark Eldar can put out, cover should not be a problem. Also, most armies tend to be Space Marines, which means 3+ Armor Saves so cover is usually not a factor.
3) The general consensus is not because the strengths of the Dark Eldar are mobility and speed coupled with vehicles bristling with firepower.
4) That said, you should have 8+ Vehicles at 1500 points, unless you are trying foot-dar, a webway porthole/coven list, or a Reaver Jetbike army a la a certain moderator on this forum.
If I were your wallet, I would return one box of Incubi, one box of Warriors, and buy the Battle Force. That way, you get the same number of Warriors, some Wyches, Reaver Jetbikes, and a Transport. One the one hand, you have fewer Incubi and are spending more money. On the other, you get way more models at a 20% discount from GW (US prices). You can get it for less through Amazon for ~$90. The original has 20 Warriors, 5 Reaver Jetbikes, and 1 Raider so keep your eyes open.
With Venoms, you can put together a decent troop choice (5 Kabalite Warriors with Blaster in Venom with 2 Splinter Cannons) for 125 points and $44.5. For comparison, a squad of 10 Kabalites in a Raider costs 160 points + and $66.25.
5) Mechanized or hybrid leaning toward mechanized is the standard answer. Some people have pioneered Coven, Harliquen, and Jetbike armies with success.
6) I generally do not run special characters although the Duke looks pretty awesome. May people swear by Baron because he is extremely cheap and brings a lot of bonuses to the army. That said, you need some unit to attach him to (Hellions and Beast Masters... Grotesques...?)
Hope that helps.