You definitely shouldn't have played Knight before the others, it'll spoil many plot-lines, you probably had no idea what many of the references in Knight were about and it'll be weird to go to older gameplay. Also, you should pick up Arkham Origins, which is a prequel and has (in my opinion) the best story. Play it after City. In retrospect, Knight has by far the weakest story of the bunch, with extremely predictable twists.
Yes. However, keep in mind that it is not seamless and Asylum is not an open world/city, instead, it takes place in a closed off area.
No. The playable area from Arkham Knight is a different area than the other games.
Yes, if not longer. All of the games have side missions.
Yes, the boss fights in the other games are miles ahead of those in Knight, especially City and Origins.
Yes, there are a lot of enemies on rooftops in Origins and I believe a handful in City.
Return to Arkham includes all DLC and Catwoman's DLC is integrated into the main plot of City. When I played the GOTY version, her missions were just included in the main story and you seamlessly switch between her and Batman at certain points.
Yes, and they're way better and longer than the Arkham Knight DLC. "Cold, Cold Heart" is the Origins DLC and it's AMAZING.
I believe she can explore pretty much all of the area in Arkham City.
No, it is only challenge maps, there is no story or free roam.