I think they technically say that Vulcans don't lie, not that Vulcans can't lie. That would imply that they prefer to avoid it, but can if they need to. I mean, if Tuvok couldn't lie then he never would have been able to go under cover as a member of the Maquis.
DS9 is a Bajoran station, not a Federation one. The Bajoran economy is not post-scarcity and still runs on money. Either Starfleet officers get a stipend to purchase things when posted on such assignments, or Quark simply bills Starfleet. Either way, Starfleet/the UFP likely has a reserve of latinum and other resources for trade with other nations.
They didn't want to fire her, but she did want to quit. She wasn't happy with the direction they were taking her character. I wouldn't be surprised if she also had issues with the same guy McFadden did. Jadzia was killed off because Berman wouldn't let Farrell switch to being a recurring rather than a regular, which may be what you're thinking of.
And a malfunction has the potential to destroy all life in the multiverse.
I didn't like that part at all. An infinite multiverse, which they state in DSC is the case, means that anything with a probability greater than zero is guaranteed. Mathematically, the multiverse should have already been wiped out at some point. It's also a throwaway line meant to increase dramatic tension for all of ten seconds before the scene ends, and an empty threat given that following through would end the show.
They actually did. Remember the Relativity? They talk a big game but, like the regular Prime Directive, the Temporal Prime Directive is secondary to the continued existence of the Federation. That's why there wasn't a peep out of them when Kirk stole some whales from the past.
Depends on the distance being traveled by both ships. The Milky Way is 1000 light years deep, so there's a lot of vertical room to maneuver. Mentioned locations at real star systems, like Wolf 359, are definitely not all on the same plane in any way. Possibly more relevant, though, is that 'up' isn't really much of a thing. Star systems can (and do) have their axis tilted significantly off of the galactic axis, so even if you define 'up' within a star system and orient your ship that way, you may wind up tilted weird when you arrive at the next system due to it having a different 'up'. You could define 'up' by the galactic axis, but that would still only apply to the one organization; there's no reason for the UFP, Romulans, Klingons, Cardassians, and Dominion to all agree that one side of the galaxy is the top and the other is the bottom, but they do anyway. Humans couldn't even agree on which way to orient maps of our own planet for centuries.
SNW actually uses warmer lighting than this DSC shot, which helps the set look much more like an updated version of TOS's bridge set.
I don't think that's too big of a concern, to be honest. You can't negotiate with a spacial rift and the show handles that kind of thing fine. I think they were having problems with First Contact's script and decided to solve it with a named antagonist rather than just hordes of Borg.
She wasn't too bad in First Contact. The movie implied that she was simply an avatar for the Collective, not too different from Locutus. Later writers didn't get that and VOY turned her into an individual within the Collective who controlled all of it, somehow. Then her depiction just kept getting further and further from her depiction in First Contact, mostly keeping superficial things.
Section 31 went through a very similar shift, where DS9 implies that Sloan and S31 are rogue agents and Sloan is talking out of his ass in regards to any real authority and taking an, at best, extremely liberal interpretation of the Starfleet Charter, then later works making them an official part of Starfleet.
I suspect she never learned how to read faces or tell tones of voice apart, which is why has so many problems when her empathic powers are supressed. She can sense sarcasm through an opaque soundproof wall, so why would she need to know that people sound different when they're being sarcastic?
Moriarty was draining enough of the Enterprise's power to cause brown outs and was using a huge chunk of the main computer's processing power. The EMH is much more efficient. He's also probably more sophisticated in other areas, like precision movement or being able to function in arbitrary non-holographic environments.
Just a reminder that she didn't actually explain why she was tearing up a picture of the Pope, she just pulled out a picture of him and tore it up without context. Nobody understood wtf was happening.