Sorry to hear about the second clown.
According to most research, whatever he had, the tang will carry too. The tang may not mind it, but he could have it. Additionally, the life cycle for Ich and Velvet (not sure about Brook), includes a stages that live in the water, in the sand, and on the fish. The tank won't be free of the pathogen until it has run fishless for 4-8 weeks.
Generally a quarantine tank shouldn't have a sand bed, rock or invertebrates in it. It just allows you to treat with meds without killing the inverts plus the pathogens don't get the opportunity to nest. Most experts recommend a water change every day. Although if not treating and only observing a new fish, water changes don't have to be daily. Some people go to the trouble to siphon out excess food and fish p00p every day. I did that sometimes.
For my formalin plan Iwould use 3 gallons of QT water in a bucket with a powerhead and airstone. If gave me a daily opportunity to siphon out the qt tank waster and do a water change. While the fish is getting dipped, it give me some time to put new water into his tank.
Copper is easier, just add it to the tank at the recommended dose and maintain that concentraion during the treatment period.
The problem in all of this is that it's really hard to diagnose the problem and all of the advise from the experts is very conservative, so it's imposslbe to know when a fish is cured. The safe standard seems to be 6 weeks of observation with no issues. That starts at the conclusion of treatment.
Keep in mind, I didn't follow much of the advice.
I just wish the state of the live stock in the hobby were healthier. Putting a new fish in your tank shouldn't be Russian Roulette.
Why are fish arriving at stores so sickly? Why do so many fish get sick at stores? It seems there is little insentive for a LFS owner to cleanse his system and trash his livestock the first time he sees Ich. He just needs to keep stuff long enough to sell it, so he just throws some copper in his fish only supply and figures he's making an effort to treat incoming fish to some extent. And then the hobbyist gets the fish home and it looks fine for a week, or maybe two, or maybe even three, and then it comes down with something.
Or the fish may not have a pathogen, but simply not have a strong ticker after all of the stress of capture, whether through mechanical means or chemical means.
It's just a pain in the arse all around.
I think I'm done with fish, I've got enough, only corals for now.
Cheers
Josh