While I agree that currently dealing with dungeons is probably easier with 5x DPS, just bursting through it, we do have to keep in mind that even in Tanaan gear you can outgear these instances by something like 60-70 ilvl. I seriously doubt that playing the instances at intended gear levels (at max 630 in the case of Heroics, or 680 in Mythics, no legendaries) is always easier as just 5 DPS. So looking a head to legion, you do have consider that DPSing through everything might not be an option to begin with.

Similarly to Andrea, I also found more enjoyment in playing as all roles in instances, although I absolutely adored my 4x Ret 1x Prot paladin team for dungeons as well. Sadly with the upcoming nerfs to off-healing on Pallies, I don't know viable this setup will be anymore.

As far as the actual questions by OP:

1. As others have mentioned, adding another class usually means you do have X amount of new things you need to be aware of, or choose to lose efficiency by ignoring them. How much each one adds is very dependant on the spec. Some need fairly little baby sitting to perform adequately, while some require constant attention to fulfill their potential.

2. The main advantages, in my opinion, are in terms of utility (portals, lock cookies, life grip, mass invisibility, etc) and FUN. While hunters currently outperform anything else in the DPS role (for consistant single target anyways), it simply is not as fun as having a variety of classes and spells going off.

That being said, class stacking is just as viable as buffs are basically non-existant in Legion and the introduction of personal looting methods means your characters won't be fighting over gear upgrades even if they use the same type. Additionally having less class halls to deal with is a bonus.

3. All of them should be viable. Monk perhaps needs the most attention out of the 3 due to the stagger mechanic, while Warrior and Bear tanks can be made a bit more passive in your setup. Exact numbers for which perform the best are really not available, so take this with a grain of salt.