I'm going to hit a couple specific questions here.
Tap Water - The issue is not algae. Sure, some cities have nitrates and phosphates in the tap, but that is not the real issue. Can you be absolutely certain your city's tap water contains no copper, iron, zinc, etc etc etc? Some places even have heavy metals such as lead. Now, odds are that if any of these metals or other compounds are present, the quantities will be miniscule. And as such, you could top off with tap for a year and have no problem, as the metals will bind with the rock and sand. However, eventually, there WILL be a saturation point reached. One day, you'll add a bucket of tap water and a year's worth of copper will explode out of the sand and rocks, killing all the inverts in a day. For every horror story, there are at least two people who will say "That's ridiculous. I've been doing that for years with no problem." but do you want to take that chance? You can get top off water for 20- 40 cents per gallon at a grocery store. I use the Glacier brand dispensers. It is worth it.
Tangs - Yes, yes, yes. Joe Schmoe keeps a regal tang and a yellow in a 30 gallon tank and they've been fine for a year. Of course, their internal organs are slowly crushing each other as their skeletons' growth slows down in such a cramped space. Even if later transferred to a larger tank, that animal's lifespan has been cut in half and it's quality of life significantly diminished. I am not the Tang Police, but not even a juvenile Tang should ever be kept in a 55.
As fish grow, they secrete a chemical signature into the water that inhibits their own growth. In a significantly large body of water (ocean), this is instantly diluted and has no effect. However, in confined spaces, or with large populations, it slows they skeletal growth. This is an adaptation to prevent a species from eating itself out of house and home. The problem is that the chemical's effect is limited. It can slow growth, but only so much, and not completely. A Tang kept in a small tank WILL eventually have severe physical deformities and die early.
*cue the protest from a guy who's kept a tang in a small tank for two years* Yeah, I heard you. It's been two years. A human can survive two years in a closet. But 50 years later, they will still be paying for the trauma. Don't. Do. It.
Blue and Pink Sea Star - Pick a different species. Period. This is a sand sifter, and even in a large tank, it will eventually kill all the beneficial organisms in the sand bed and starve. And it won't even have the decency to die where you can see it. It'll bury itself and rot under the sand. Try a Fromia star. They come in very pretty colors. But as stated earlier, wait months.
Damsel - You'll be trying to get it out of the tank eventually. They're mean. A good small blue fish is the Chalk Basslet. And you can have more than one if introduced simultaneously!
Those rocks are simply base rock. They will become live rock over time. Keep em!
Butterflyfish are hit or miss. Most are considered "Reef Safe with Caution" with means "Probably ok. But they might go on a coral binge one day and eat everything."
My foxface does quite well in a 55, and he eats all kinds of algae, even bubble algae!
You can have way more snails in that tank, plus some hermits. I strongly recommend Nassarius snails, too, as they keep the top inch of sand stirred, and are great at cleaning up extra food.
Whew! Sorry that was long winded!
YT damsels I've heard can be very mean, so personally I stay away from damsels (except my clown of course 
