Admittedly, in that model of viewing Trek, we can't even tell what the registry number of the Horatio might be, so whether she's first batch, second batch, third batch or the rare pink three-and-a-half-nacelled variant is left even more obscure than otherwise.
Don't you mean the Niagara class? Ugly thing hehehe
No way of really knowing what ships make up a fleet really. The battle to retake DS9 supposedly had Olympic class ships in the fleet (according to the defiant screenshots), so really it is quite circumstantial and wouldn't be surprised if a few Constellation class and Ambassador class ships were there supposed to be somewhere in the background as well.