If they had the means, coudl they develope a ship as powerful as the Galaxy-class, Vorcha-class, D'drieniex-class?
I'm not too sure what you're asking here. You ask could they build such a ship "if they had the means". However, if we assume they have the means then obviously they
could build such a vessel.
I think you mean "do they have the means?" In which case, I'd say yes. The choose not to due to their style of combat revolving more around large numbers of small, cheap, mass producable vessels that can outnumber their oponents.
? If so, what would it look like
Presumably a scaled-up version of a Galor, I'd assume.
and how many could be produced?
This is going to be difficult to figure out, though not impossible.
First, let's assume the Cardies are going to cut the numbers of Galors and Keldons in production by half, and use those resources to build thier new battleship.
Now, the DS9 TM (non canon, I know, but let's roll with it) says the Cardies produce "63 Galor class battlecruisers [and] 15 Galor class warships" per year.
Presumably, the battlecruiser is
the standard Galor listed on DITL and the warship variant is
the Keldon, which GK points out is just a modified Galor.
Okay, so we have numbers. Now we need to find out how much tonnage that is.
Going from DITL's estimates, Galors mass 1,687,000 metric tons while Keldons mass 2,230,000 tons.
1,687,000 X 63 = 106,281,000 tons
2,230,000 X 15 = 33,450,000 tons
Total tonnage per year = 139,731,000
Now, if we assume that the Cardies use half that tonnage to create their new battleships, that gives us 69,865,500 metric tons. Now let's assume the Cardies' new battleship is going to have roughly the same mass as the GCS.
GCS mass = 4,960,000
69,865,500 / 4,960,000 = 14 (rounding the ridiculously small decimals down).
Therefore, by sacraficing half of their Keldon and Galor production, the Cardies could build 14 battleships annualy.
Cardie ships are usualy built for long life, so let's assume that the ship's expected hull life is 30 years (lower than DITL's estimate for either the Keldon or the Galor to reflect the difficulty in maintaining such a ship).
30 X 14 = 420
Ergo, by sacraficing half their production capacity of Galors and Keldons, the Cardies could maintain a fleet of 420 battleships.