Yes, but very slowly and I don't know how to improve adaptation. Once they are adapted they grow more slowly but normal. The key is to get new skeletal growth at all. Iodine may help, keeping the iodine concentration rather on the high side at 60 to 100 ppb but on the low side. But this is a bit speculative from my side, some observations but not well tested yet.
For the old part of the skeleton the prognosis is quite bad. I call it the "memory effect of the coral skeleton". Maybe it is the organic matrix, maybe it is the mineral structure of the old skeleton, but something seems to inhibit new growth on the old skeleton when phosphat concentrations drop. The best chance for new skeletal growth is on the growth tips and the growth zones. From there the corals may initiate new growth adapted to low phosphate concentrations.
Yes, but in the oceans it is a much bigger problem. The problem in the oceans is that nitrate has two effects: 1) It supports algal growth which competes with coral growth for space and nutrients, especially phosphate and 2) it causes direct damage to the corals, especially when they are in short supply of ammonium and phosphate, which is caused by 1)!
In tanks in the best case it works as an oxidant like hydrogen peroxide killing cyanobacteria. In many tanks it is just chasing numbers without any effect. The nutrient load in the water is high and, if at all, coral growth is limited and reduced by trace elements. No macro nutrients limiting coral growth, corals hardly make use of nitrate as a nutrient. No nitrate effects to the corals.
Yes, for sure! The bad thing is that amino acids also feed opportunistic bacteria, rotting bacteria, which may attack also living tissue when they get abundant. So rather be careful with amino acids.