I think the warp core's size is directly linked to the power requirements for the ship, so the size of the nacelles needed to move the ship determines how powerful the warp reactor needs to be. Thus it becomes about mass and size, since a larger ship needs a larger field. As for two warp fields interacting I think they would repel each other, as Enterprise and Columbia experienced some turbulence when their warp fields merged, it'd make sense that the spacial distortions (which is what warp fields are) wouldn't interact that well, if at all. That's where the precise measurements for interacting with warp fields are needed, since the field would work with a certain frequency and shape you'd need to know both to merge with the warp fields of another ship.
In any case the ships aren't accelerating, they're generating a warp field that changes the way that space interacts with their ship, with a decrease in what is essentially mass in front of the ship and an increase behind, thus creating a constant falling sort of motion. It'd be the same as generating a hill behind an object and a hole in front of it, it's going to roll down, in simplistic terms. Because the ships aren't actually moving, there's no resistance, the increases in energy for each consecutive warp factor are related to the degree of warping of space you want to achieve, so it takes more energy to create a warp field for warp 6 than warp 5 because, metaphorically, the hole in front of the ship is deeper and the hill behind it is taller.
I think that's very unique due to the ships being the same mass and volume. I remember wondering why the other ship didn't shut the drive off completely too, maybe the sabotage were preventing that, but did allow lowering power, combined with a movie Speed like thing where if they slow down something worse happens. So, they did the sustainer thing to keep speed steady while lowering power to trick the sabotage. The episode is "Divergence" and the below link as a picture of the two ship's fields touching. They have about as much extra volume as I thought they would as based on the escape pods, a little more actually.
Whilst that could be the case I think it'd be possible to have 2 different ships match warp fields, it'd just be difficult, with significant communication and computational power needed. Take the Equinox and Voyager, when they were together Voyager had to extend her shields around the Equinox, so they were flying in close formation. It'd be reasonable that to maintain the shields they'd also have to stay close enough that they'd have to merge warp fields. Now we don't know if they warped anywhere together in that formation, but if they had needed to, like if they couldn't get the aliens to stop attacking and had to travel back to the Alpha quadrant like that, then they would have had to go to warp in that formation, or they'd risk losing the shields. Thus it'd be reasonable that they'd be able to merge warp fields, even though Voyager is at least twice the size of the Equinox. Now it's possible that it wasn't mentioned in the show because none of the writers thought of it (that'd be my bet), but I still maintain that it's possible to merge warp fields, but like shields you have to have both ships do it, and they have to share information to do it.
I think that's generally the case. When tracking ships who are long gone they generally look for the telltale signs of warp passage and weapon usage. The only problem here is the high energy field should leave a powerful trail that the small vessel can't compensate. The difference would be you would need to find the trail. The other issue I have is, just how active does the ship's warp core need to be to lead to long range detection? The warp core constantly create exotic emissions while running not just when running the engines.
I agree, a lot of long range sensing is probably passive. The major reason I believe this to be the case is Voyager's astrometrics lab. They sent a signal to the Federation on their first day and it was supposed to take years to arrive, but then they scanned their entire expected trip several seasons later, which would still be tens of thousands of light years, and took 1,000 light years off the trip. The only way they could get improved data is if they collected it passively, when signal propagation is considered, otherwise the data collection should have taken over a decade.
I think their short range sensor range is the practical limit of active scanning. Here's the interesting thing, sometimes the ships are so far away from anything they don't have real time communication, but as long as they are near a relay they can have real time communication. Logically, with versatile enough relays, the short range sensors should be able to use the relays to bounce their signal both ways. Same for any ships in the area.
A high energy field certainly, but once the shuttle leaves the influence of the parent ship the field would degrade to the point that the shuttle could maintain it, at whatever power level they have chosen. On top of that in all the cases we've seen that have general purpose ships trying to hide their warp trail they haven't been able to do it for powerful fields, but there have been cases where specialized ships have been able to hide their warp trail, perhaps the shuttle could be fitted with some equipment to do a better job. Hiding the warp trail also only really applies if the enemy had already discovered that the shuttle had been there, in which case the shuttles mission would likely be compromised. The long range sensors on ships only seem to be good at detecting the power form ships, not warp fields, certainly not on the scale of a shuttle at more than a few light years. When there are large groups of ships traveling together, even if they're cloaked, then you'd probably be able to pick up the distortions from the warp fields, but it's mainly the power from the warp core that the sensors would detect.
As for the relay stations, I'd guess that much like modern communications equipment they're designed for specific frequencies, ones with minimal interference and high penetration. Not to mention the huge bandwidth needed to transmit the raw search information, since the relay station wouldn't have the processing requirements or specialized hardware for sensor analysis. They'd probably be given short range sensors, mainly to detect something like a meteorite, but they'd be nowhere near a starship grade sensor array.
It seems simpler to just turn the ship and have the field follow. Since the field is constantly renewed, the field will be created with the new heading as the ship turns. Consider this, what is the field turning again? In space there is nothing to turn against, so an uneven field should actually go off in the direction of the imbalance, rather than turn. Although, it's reasonable that it may be pushing against either nacelle unevenly. But, that doesn't explain how single nacelle ships can turn and I don't like the idea of creating turn forces along its length.
That depends on how long it'd take space to adjust to the rotation, the warp field is, as I stated earlier, digging a hole in front of the ship, so moving the whole relative to the ship would take time, slowing down the turn. It also depends on whether a ship can turn with it's sublight engines at warp, if they would even have an effect, and I'm not sure whether they would. If my idea about warp fields holds then I'd suspect that trying to turn with the sublight engines would either turn the ship, but would have to be done slowly, or would collapse the field because of the sudden change in the warp field geometry relative to the spacial distortions. That'd be why they can't turn quickly, otherwise the field would collapse.
