Glad to hear you managed to get your fish out, even if it meant dismantling your tank. I had to do it on a 55 and it was a huge pain, can't imagine doing it on a 200.
To answer some of the questions.
Water changes on a quarantine tank containing copper. Put a seachem ammonia alert badge in the tank. Standard ammonia tests can give inaccurate readings with copper, the badge is accurate. If you have some sort of biofilter to get rid of the ammonia, no you don't have to do water changes. Just be sure to top it up regularly. I'd mark a line on the glass so you know exactly where to fill up to and don't go over it or you can drop your copper levels below the therapeutic range and you'll have to reset the counter. However if there is no biofilter, you cannot use ammonia reducing agents like Prime, this will react with the copper turning it very toxic, so you may have to do water changes. If you do, make sure you dose the new water with the same levels of copper as the tank BEFORE adding it in.
With your fallow period. Double and triple check for your missing fish. On the floor, behind the tank, overflows, filters, everywhere. Even check they did not come out with your rock, hiding in a crevice. If a single fish stays in your display the fallow period won't start until after it dies or is removed. Once you verify no living fish remains in the display, you can put all your rock and coral and even your inverts back into the tank and refill. I don't know much about feeding corals, but you may have to do so. Ensure absolutely no cross contamination either, a single droplet of water makes it from the QT to the display and the fallow period needs to be reset. The fallow period for Velvet is recommended at a minimum of 45 days.
Wrasse Sleeping. Fill a tray or other container just big enough to comfortably hold the wrasse with sand and put it in the QT. It's not ideal, and it will mess with your copper levels a bit, but such a small amount shouldn't pose a huge problem.
For ramping up the copper levels in your QT. You'll get lots of different answers on that one. Really it depends on how your fish are doing. Slower is always better with copper, it's nasty stuff. However, if the velvet is bad, you may not have the luxury of time. If they're showing the other symptoms of velvet, swimming into flow, light sensitivity, rapid breathing you may want to bring it up to therapeutic range over 2-3 days, using a freshwater dip as needed. If they're acting more or less normally, you may want to stretch it out over 5-6 days. Again, watching for any signs of respiratory distress. I would also pick up a copper test kit if you haven't already. Relying on the dosage instructions alone isn't good as tank water volume is never exactly what it says its supposed to be. Any kit will do, however everybody here, including myself will recommend the Hanna High Range Copper Checker. Accurate results on a digital readout, no guessing on a colour chart.
I will also add as a bit of a disclaimer, I am no expert on this subject, and I am certain other, more informed people will give you better advice on how to proceed. I'm just going off what I have read here, and my own experience with Velvet.