Multiples of all yes. Unknown Dungeon consists of the highest available Pokemon in the wild plus Mewtwo. The whole area isn't even available until after defeating the Elite 4. That is the reason the legendaries are placed there. The birds are extremely rare and just as difficult to catch as usual. I found it more intense than their normally scripted first encounters. Normally you can save and retry often without much grief. Here you get a little more pressure knowing if you encounter one, it could be many more random encounters before you see another. Especially if you want a second Mewtwo. I had captured 8 Moltres with many more failures than that before I found one randomly encountered Mewtwo.
Once I become more experienced I plan on coming back and improving the system. I don't know when that'd be though.