I just had an awesome Arena experience. For reasons unknown, it started as a three on 3, but two people left over the course of the battle, so it ended up as a 2 on 2.
But in both phases of the game, it was so much more fun than the 5 on 5 you usually get. Nobody exploded instantly because combined fire from both sides just would not add up to such high numbers.
The whole battle felt a lot more like Trek on the shows, too... because there, you rarely have 5on5s, but either a maximum of two or three ships from each side... or hundreds. Hell, even in the STO missions your opponents are rarely that many ships of your own tier, even when teaming up.
Could I change one thing in PvP arena combat, then it would be to add battlegrounds to the queues where there are no more than 3 ships on each side.
And sometimes, you'll end up with three cruisers against 3 BoPs/Raptors, and the Klingons will do hit and runs, picking you off one at a time because with only three of you, you can't out-heal their alpha strikes... *Insert evil chortling here*
But yeah, I think a lot of people would be up for smaller battles, as long as it wasn't a total cruiser-fest. (Although I think a lot of Klingons would be okay if the Fed side brought all cruisers.)
No, you don't get credit for private matches, unfortunately. (I can see the logic on why not, but it wouldn't be any more abused than the AFKers are already abusing PvP right now...)
Yes you do. Every 3 arena matches, even if it is only to a kill count of 5, will give you credit to your Dil Quest. I even recently tried to see just how quickly you could have 1 escort blow up 5 ships to do some farming in private matches. It worked.