- What happens if a fleet is in transit via Vasari phase stabilizer, and one or both of the endpoint PSs is destroyed (or, in the case of a Marauder's temporary PS, expires) or temporarily disabled (by special ability, e.g. another Vasari player's Kostura Cannon)?
If the fleet is already mid-jump, nothing will happen. They'll arrive at their destination normally 
- Is there ever a situation where adding another one in the same gravity well adds more income due to some per-portcapacity limitation, like trade ship production, or a cap on the routes serviceable by a single port in a gravity well?
Are you talking trade ports here, or what? Trade ports stack linearly. Each port adds a certain amount of trade income, assuming of course there's any other port not in the same grav well for the trade ships to go to. It does not need to be a 1:1 relationship, so you don't need 3 ports on one planet to be able to service 3 ports on another. You can have 5 ports on one and 1 on another, it won't matter.
- Do any or all items which required specific research for a given use (which in turn required X number of labs of a given type to obtain) require the same X number of labs to perform those abilities? I seem to recall that experimenting with eliminating a weapons lab and losing the ability to fire an already-constructed Novalith, but I could be mis-remembering. Cruisers clearly don't shut down if all labs have been trashed, but loss of specific special abilities might be happening, I suppose.
All passives remain in effect if you lose the required number of labs for the research. You only lose the ability to build new hulls/buildings, and operate superweapons. So if you have 5 labs for those heavy cruisers and you lose one, all the weapon/armor/shield techs will stay in effect, you just won't be able to build new cruisers until you get the required number of labs back.
- Is it entirely correct that hull damage (purely -- ignoring the specific affects of various special abilities) has zero impact on how well a ship functions, until it is completely destroyed? i.e. turns, moves, fires, builds fighters, responsiveness to orders, no experience penalties due to crew death, et al with full speed and ability? The weapon damage estimates don't go down, I've noticed, suggesting that offensive abilities are unharmed, but there might be something subtler that I could miss.
That is entirely correct, hull damage has no negative impact on ship performance.
