Yes! It is possible to use HaxeFlixel as a framework for a 2D MMORPG. I've made a 2D MMORPG using HaxeFlixel and it's been great, I've never had any regrets about choosing HaxeFlixel and would use it again if I was starting a new 2D MMORPG project. If you'd like to check out my game as an example of an MMORPG made with HaxeFlixel, you can find it here: http://www.portalwalker.com
FlxGroup can be added to other groups/states, so update() and draw() are called on all the members of the group with exists == true. Be careful, adding to two groups can lead to update() called twice resulting in 2x simulation speed (can be solved by marking the group active = false).
Use arrays when you don't want to update/draw sprites, or they are updated/drawn from other group already.
And also, as you said, use groups when APIs demand FlxGroup, like for object recycling or collision.
It's not slightly worse, it's a lot worse. Don't measure with fps, measure with milliseconds, they tend to accumulate the more code you have, and if they accumulate more than 16 ms per frame, the player will have less than 60 fps. If you have steady 60 fps, but with steady 15 ms (draw + update), you're in trouble.
Because it would be the slowest part of rendering. My example may not be the best, because copyPixels in new versions of OpenFL is really slow anyway, so you don't want to use it unless you are ready to do some optimization work on it
Note that I'm talking about native targets, flash target is mostly unchanged AFAIK