4" (from rostrum to tail/excluding claws) is common, but you can see them larger than that. I've had several get to about 6", and they get fairly bulky as they get older.
Generally, they thrive in warmer waters but there are invasive, stable, populations farther North than me so your water isn't really an issue. Though, personally I'd raise it up into the 70s but it's not necessary. The jacks and the cat are likely to eat it at some point (probably when it molts) or vice versa when it gets larger. This species is pretty aggressive and actively hunts and your jacks and cat both like to eat crayfish. But with enough hiding spaces/rockwork/etc that may work out alright.
If you want to sex it, the most definitive way it to take it out and look at/for the gonopods... you can use this for reference:
http://www.crayfishworld.com/sexy.htm
You'll be using the 2nd and 3rd photo sets for the kind you have.