I have not the slightest clue about the egg, since I do not have much experience in that region, but my guess would be no, the shark is fine. You may want to take that question to the aggressive board since there is a ton of people who really know their stuff there.
As for the puffer, you will want to do a quarantine and hypo. However, the problem here is that there is no biological bacteria in the refuge. As soon as you cut that refuge off, you will begin a cycle on that tank because there will be no bacteria in the tank to break the waste down from ammonia to nitrite to nitrate.
Also, if you use live rock from your main tank, you will kill that rock during hypo. My best suggestion would be to get a cheap hang on the back biowheel filter, let that run on the fuge for 3 or 4 days to begin to accumulate bacteria, and then cut off the fuge and begin hypo treatments.Pick up a bottle of Turbo Start, just in case a mini-cycle occurs. This way, you have a biological filter on the fuge to support the puffer, and you have more bacteria readily available just in case there is not enough on the biowheel.
Another problem is that the ich is now in your main tank. Hypo-ing the puffer will help the puffer, but once you put the puffer right back into the main tank, there is a possibility of him contracting the ich again because you are doing nothing to kill the ich in the main tank. There is five fish in there that the ich could live off of if it wanted to. It is choosing the puffer because that is the fish with the weakest immune system right now. The ich knows that the puffer will put up less of a fight.
