No.

No, you can't field these types of Dogs of War characters unless you're a Dogs of War army.

As named standard bearers from Regiments of Renown are classified as characters they should be handled as Battle Standard Bearers in terms of capturing / losing banners.

No. The Warhammer Design Team has specifically stated that impact hits always happen before everything else in a combat, unless specifically noted otherwise. Therefore chariot impact hits qualify as a being "entitled to strike first because of a special ability" which per the rules for pikes "will still strike before pike-armed models."

Provided the unit has enough ranks, four ranks if the unit was stationary or three ranks if the unit charged that turn as is outlined in the Fight In Ranks section of the Warhammer Rulebook. Note that in cases where a pikemen unit consists of three ranks or less, all the ranks will fight when engaged with an enemy unit to their front, regardless of whether the unit was stationary or charged that turn.

No. The reference in the Paymaster's rules directs players to treat the keys to the pay chest like a Battle Standard. Note that nowhere in the Rulebook does it state that a Battle Standard Bearer is entitled to carry a magic banner. It is the existing army books which explicitly state that Battle Standard Bearers may carry magic banners. The Paymaster is not explicitly given the ability to carry a magic banner in the Dogs of War army list, therefore, he may not.

The intention of the rules is that no, Undead units cannot be joined by non-Undead characters and vice versa.

Since the "Festooned With Pistols" special rule for the unit states they "gain an additional attack because they are fighting with a pistol in each hand", you should add 1 to the Attacks value in the displayed statline. Thus, Long Drong has 3+1=4 Attacks and each Pirate has 1+1=2 Attacks.

The Festooned with Pistols rule explicitly grants the unit S4 & armour piercing to all of the unit's attacks. Thus the unit has S4 armour piercing attacks in close combat.

Yes. the Slayer Pirates have "two or more pistols" and thus may fire 2x multiple shots with their pistols in the Shooting phase.

Yes, all of the Dwarf special rules (Ancestral Grudge, Relentless, and Resolute) apply to Dwarf Dogs of War.

Yes, 3+ Scaly Skin save like most Dragons.

Asarnil is worth 130 VPs, his Dragon is worth 330 VPs.

No only the leader counts (Asarnil and Hengist), in the cases you mentioned.

In the Warhammer Annual 2002.

In the Warhammer Annual 2002.

In Warhammer Chronicles 2003.

In White Dwarf Magazine

Warhammer Chronicles 2003.

No.

Certainly not!