1) We have no idea how many Warbirds they have. We see a bunch during the Dominion War, but I don't think we ever see more than five or six at a time. Contrast this with the thousands of Starships we know the Federation has.

Do we know that the Federation has thousands of ships?

I'm on my most recent rewatch and the battle with the Borg at Wolf 359 practically crippled the Federation. To my knowledge, Starfleet lost 39 ships and about 10,000 people. There are numerous points where Picard is left to bluff and the ships we see are smaller and less likely to end up in a battle. And in other episodes we see admirals needing to come out of retirement.

By season 5 in Redemption pt 1 and 2, we see the Klingon civil war and the Federation barely has 21 ships to form a net on the Klingon-Romulan border, and most those ships were in drydock or undergoing repairs, not to mention they were so severely understaffed that the Enterprise had to loan out bridge officers to command and her supplemental crew staffed most if those ships.

I know that the Federation rushes out ships after that, but I dont ever recall there being more than a few dozen that are actually capable for war, including the Enterprise. I know we see more ships, but most of them appear to be science, escort, transport, or other random noncombat missions. I'm led to believe that the actual number of Starfleet ships is in the low hundreds, specifically limited to couple hundred. Where as only 30-50 are in actual fighting shape. Or shape enough to go into battle and take and dish out a few hits and not be completely useless.

Forgive me if my memory is just failing me, I can't for the life of me remember a lot of the DS9 encounters and the Federation's fleet status.