Yeah, you can mix those tangs so long as your tank is a 180 or larger (270 is good). The issue you'll run in to if you don't quarantine and treat every fish before going in the DT is, well, death. Powder blues cannot live in any other environment they're very very fragile with very thin slime coats. They're exponentially harder to keep without sitting in therapeutic levels of CP or Copper for a full 30 days then observed to ensure the parasites are gone.
Your regal tang cannot handle CP, so I would use copper. I would add the three tangs at the same time. If not, I'd add the hippo then the yellow and powder blue at the same time.
If you do an eel, it'll need to be treated with CP, as they cannot handle copper.
You'll need to treat all fish that ever go in, because if not they'll carry diseases that will jump on the tangs, despite no symptoms being shown.
Also, with a tank that big 3 tangs are actually MORE likely to fight because carving out three territories is actually possible-- so they'll try. I'd almost recommend a trio of zebrasoma (yellow, sailfin or deskardini sailfin, purple, scopas, black, etc) of different species and the PBT and Hippo. They'll have to spread aggression more this way. It'll be harder to carve the tank out and be territorial, similar to how we do with African cichlids only these fish are more dangerous.
Sounds like a beautiful tank plan!
