CAT FIGHT !

Great name!!!!

You're going to need a shed-monster style comb. (Doesn't have to be that brand specifically but a comb that looks kind of like a little rake, with rounded finger-like metal hooks that will glide over your hand smoothly. Some pet stores only seem to carry them in the dog aisle though.) It'll get the most fur and mats out with the least pulling and doesn't scratch the skin, and cats actually like being groomed with those. You still have to pace the effort so it doesn't pull too much, but once that is worked out you may have a new best friend. Regular combs or other style thatching combs pull or scratch too much, and you usually end up with an angry kitty instead of a happy one. After the first combing and removing what seems to be an entire cat's worth of hair (those combs really work vs. other brushes and combs, particularly on the undercoat), it's about a weekly or bi-weekly thing depending on how fast the cat sheds. Later efforts aren't as impressive in terms of quantity, but it'll help the furniture stay nice.

As for ending any territorial arguements, a glass of water and wetting and flicking your fingers does the job with most cats. The average cat hates getting wet to the point where they'll give up without too much trouble, even though there's barely any water being used. Better and less abusive than trying to manhandle or otherwise force a non-cooperative and onery cat to move. Cat doesn't get roughed up, and neither do you. And unlike the spray-bottle approach, the water-flick gesture by itself (with no water) will eventually start to work. (Because the cat associates the water coming off your hand rather than being from the spray bottle.)

And of course every cat is different. They really are individuals. Some attach right away and need almost as much attention as dogs, others are a bit aloof and take a while to build a relationship with their people. Some are quick learners, and others dumb as a brick. Usually if the relationship is rewarding enough for the cat, they'll be plenty willing to work with you.