Can heroes attached to threatened units make missile attacks during the extra initative passes?
A hero can make missile attacks if he is not threatened. A hero is not threatened by an enemy unit unless an enemy hero is attached to the enemy unit. So the answer is that the hero can make missile attacks during the extra initiative passes IF the enemy unit that is threatening the unit he is attached to does not contain an enemy hero.
Keep in mind that if a hero is leading from the rear, he has a visibility distance of 0 hexes. Given that Bobloblah didn't know that heroes would receive multiple attacks, it would likely be kind to allow him to assume that attached heroes he hasn't attacked with are currently leading from the rear. There's no particular advantage to leading from the front if you're not about to fight - it just makes you vulnerable.
If attached heroes attack the same target as their unit, do they also attack in the same way, or can Jagtai use his bow while his unit uses melee, as long as he attacks the same target?
The hero can make whatever attacks he is eligible to make. Jagatai can use his bow provided he is not threatened.
Does the prohibition on wizards casting a spell the same turn they moved apply to the extra passes as well?
According to the rules-as-written, in order to cast a spell you must have remained stationary in the movement sequence of the turn. This would apply to all bonus attack sequences.
That said, the rule above was simplified from an earlier, more mathematically, accurate rule, which would actually say that you should get 2 bonus attack sequences if you walked and 1 if you hustled.
The mathematics are that each Brigade-scale D@W battle round represents 4 combat rounds and each hex is 4x the distance; a hero that moves full speed is moving full speed for 4 rounds; a hero that moves half speed is assumed to moving half for 4 rounds and thus unable to use magic (which is what the rules as written assume); but they might be moving full speed for 2 rounds and stationary for 2 rounds, and thus able to use magic. This latter interpretation got so complex that I eliminated it, but for games where you are really "zoomed in" and focusing on the PCs on the battlefield rather than the wargame aspect it can be more fun.