I am in the process of cycling a 200g tank 48x36x27. I plan on introducing a PB tang, Purple Tang and Sailfin tang all at the same time. I have read multiple times that tangs should be introduced at the same time.
That is absolutely correct, tangs should be introduced together. However, I would suggest that these should NOT be your first three fish as the tank will be immature and these fish are grazers.
My question is three fold.
1) Is the tank size/dimensions ok for the three tangs mentioned?
The tang which is behaviorally most sensitive to tank length is the Powder Blue, I would prefer them in a longer tank, ideally six feet minimum. Remember their native environment is one of high surge. Also a sailfin tang will exceed one foot, which will look strange in a four foot tank.
2) Are these 3 tangs ok to have together?
I would not put those three in a 48 inch tank. Three different tangs would work, however. Remember tank size and tangs is a function of how they perceive their territory. If they feel cramped, they will reduce their number.
3) Finally, after spending the last 3 hours in the quarantine forums, I began thinking how am I going to quarantine 3 tangs at the same time in a 29g QT tank?
I am very glad you are going to use a quarantine protocol. While not the subject for this thread (and I do not answer questions here on it), read my blog for a suggested quarantine protocol, or alternatively read the Fish Disease Forum stickies about Tank Transfer.