A good LFS would discourage you from putting tangs with Damsels.
Sorry but I don't agree with this at all. What fish will live happily together involves a lot of variables. I have a yellow tang with a neon damsel and they're best of friends being the only two fish in a 130 gallon tank so far and both being added somewhat close together. The problem with the damsel is more likely going to be in adding any new fish to my tank since the damsel has been in there long enough to be well established. If I added another type of tang right now I would be worried that the damsel would harrass him but that's no big deal as I'm preparing for this possibility. We're also setting up a 29 gallon as a QT tank so if the damsel does pick on any new fish I add we can just let him live in the 29 instead.
Yep, that's likely ich and yep, tangs are more prone to it than others. In your QT tank, not your main tank, there's several things you can do to get rid of it, hyposalinity and meds probably being the ones most folks recommend. Loads of threads right here on these boards about it for you!
Nope, your LFS shouldn't have advised that you use damsels for your cycle but most do just because they don't know better. A raw shrimp or ghost feeding are much better ways to cycle. Since the cycle is already started (maybe even done?) what's done is done though. Your cycle is complete when you see the ammonia go up then down as the nitrites go up then down as the nitrates go up. At that point you should see ammonia 0, nitrite 0, and whatever for nitrates. Do a partial water change to bring down the nitrates (as close to 0 as possible but anything up to 20 is generally considered acceptable) and only then is the tank really ready for the first fish.
I personally think you need more liverock and a skimmer would be a good investment for you. You didn't mention any kind of filtration (or else I just need to finish my coffee and missed it
). Surely you've got some kind of filtration on your tank???
Yep, raise your salinity and yep, you can use treated tap water without ill affects to the fish. The only harm in that will be you may get a terrible algae bloom. IMO, RO/DI water is worth the extra money.
Step by step? Ok, just my opinion but:
1. It might be wisest to see if you can get the damsels out of your main tank and either into another tank, give them away, sell them, give them back to the store, whatever. The longer they're in your tank the more aggressive they will probably get as they grow larger and establish that your tank is their territory making adding new fish in the future harder.
2. Move your blue to your QT tank and treat for the ich. Once you do that if you do get rid of the damsels it probably would be best to leave your main tank without fish at all for awhile to let the ich hopefully die off and help prevent outbreaks in the future.
3. Fix your water parameters such as raising your salinity.
4. If you're willing to upgrade to RO/DI water a good time to get that started is while your fish are in the QT tank. Do weekly small water changes with the RO/DI water. I started out with treated tap water, got a nasty algae bloom, and have been doing my routine water changes with RO/DI. It takes time to get back on top of it doing it this way instead of just starting all over with RO/DI then going through the cycle again but if you keep the inverts you can't afford to go through a cycle again. Just stay on top of it and eventually you'll get it.