1. I'd a) throw some rolls in there that might sway the decision making process one way or the other, be it knowledge rolls of the different factions to make one side favourable. Or make them roll negotiation/leadership to decide who makes the final decision. IC they might grudgingly follow the others orders but deep down wished to have taken a deeper path so might subvert the group in the future. This can create some cool moments in the future where the player who lost can privately message/talk to the GM and create a whole new dynamic to an encounter by adding some element from the other faction as an obstacle/extra opponents.
2. Make this a "these are the items available from EVERY vendor in this district" and you only have to create a single list of items. Generally players will have a desired object that they wish to find and not ask for a full inventory, that way you can use the Rarity rules/rolls for Streetwise etc. If it's still an issue I'd just explain to the player that it's unreasonable to keep requesting a stock list, that'd be like doing badly on a negotiation roll, then going to the next store and trying again, then again etc until they triumph and get something super cheap!!
3. Nope, the destiny point is generally used in combat to aid/hinder dice rolls but can be used for deus ex'ing something that might aid in the fight, not to simply ignore it. They could spend a destiny point for the back door to exist in the first place but would still need to wait their initiative turn to even attempt running, plus there's nothing stopping you as a GM spending a destiny point for the door to be locked and requires an action to Skulduggery the lock or Computers to slice the terminal to open it (which would use their action that turn so give the boss at least another turn before their lucky escape).