I quarantine everything when it comes to fish, especially if they're from a store. With tangs being so prone to ich, they go to the QT for hypo regardless of where they came from. I'd rather be safe than screaming, "There's ich in my 155G and now I have to treat 17 fish!" Which is what I'm doing right now because I didn't QT a fish. It takes one time and your reef becomes a nightmare.
I haven't went the homemade food route, and many people don't just because it's messy and well, I'm lazy. I feed all my tangs Emerald Entree, PE Mysis, Marine Cuisine, SFBB Angel and Butterfly mix and Ocean Nutrition Algae sheets. If your tang does not accept the algae sheets off the clip (many don't), you can try rubberbanding it to a rock. I could not get my naso to eat the algae sheets either way, so I had to start breaking the algae sheets up in my hand in an area of high flow (in front of the return pump of powerhead) and she slowly started eating it. It looked like flake food floating through the water. My Naso will now eat out of my hand from doing this, as will ALL of my fish. This can be helpful when it comes time to catch them. tangs MUST have algae in their diets EVERY DAY. They will also accept meaty foods, and these should be offered, but they need the algae for their health.
Since you asked about the hair algae: Tangs will eat a little of it, but not too much. It's not one of their preferred foods. Some tangs will eat more than others, it really depends on their taste for it. None of mine will, but I feed heavy and believe that has a lot to do with it.
If you're going to run hypo on the tank, use a very good/accurate floating hydrometer or a refractometer. I don't trust hydrometers at all and stick with refractometers, especially for performing hypo.