1. Should I split up these 3 rubber plants? One seems to be dying/dead?
2. If so, how do I go about splitting them?

Splitting would be very difficult; the roots are certainly intertangled. How about just repotting to a considerably larger pot?

If you really feel you MUST separate them, be prepared for a big mess.

1) Get a big bucket or pan and fill it deep enough to submerge the entire rootball.
2) Remove the plant from the pot and submerge it in the water.
3) shake vigorously to remove as much soil as possible. You may have to dump out the water and soil a couple of times.
4) As you shake it the plants will probably start to separate on their own. Pull them apart gently to completely separate them.

Now you're all ready to plant them in their individual pots. As you fill the pots with soil, "jiggle" them to get soil into the root mass. When the pot is full, tamp the soil slightly and add more as necessary. When I'm done repotting, I like to 'drop' the pot from about 6" a couple of times to help settle the soil. Add more soil to raise the level to about 1/2" below the top of the pot. Make sure the soil level is the same height it was originally. Don't bury the trunk. Water well and put them in a bright spot that stays warm. You will probably lose a few leaves for about a month and then get lots of new growth.

This is a good example of how radically different methods work fine. If I was going to separate them, I'd chop the root ball in half, straight-down from the top, with a shovel. Then if there is a pancake of roots at the bottom, lay each half sideways & chop that off with the shovel, then put in 2 pots.

I wouldn't consider this messy, just gardening. It would be an outside activity for me. I don't repot anything inside.

Compacted soil is something I try very hard to avoid because I used to do that & used to kill a lot more plants. Since I've been making an effort to avoid compacting the soil, plants rarely die.

Alternatively, you could cut them lower for a more bushy look. Happy to elaborate if interested.

Please be aware that latex sap will leak out when you cut into a rubber tree plant. It gives some people a rash like poison ivy and everyone should avoid getting it in their eyes.

Depending on where you live, I would transplant and then as soon as your weather permits it, put them outside (shaded at first). I don't see a dying tree in your pic, I see 3 Ficus that each wanna be huge trees and you have them in crowded pot, but I would not separate them. I don't move all my plants outside anymore, but Ficus is one I do as they really do so well outside. I have a Burgundy one I need to get outside.
P.S., So, your plant encouraged me to try to purchase the regular, GREEN form of this classic houseplant. Why are they all Burgundy now?! So weird these trends in plants. I love the Burgundy ones but would also like a green one again, now, those seem nostalgic!

You WOULD, however, lose lots more roots and leaves in the process and it would take months to recover.
I have done something similar to your approach to some Eucalyptus. I didn't have much choice since their roots were so intertwined they were inseparable. They did survive and are doing well, but I had to cut off about 2/3 of the branches and foliage. They are outdoor landscape plants, with lower immediate expectations for appearance, though.