I don't really know where to start so I will just answer the questions in order:
1. I consider a high nutrient tank, a tank that has nitrates and phosphates and other "stuff" in the water. Some of this stuff comes from keeping a larger load of fish, another thing that I would say makes a tank a high nutrient. I would consider a low nutrient tank, a tank that has next to nothing extra in the water. Most people try to set their SPS tanks up to be low nutrient... with large skimmers and many different reactors (carbon, denitrator, phosban) and also many times bare bottom (to make sure to get everything out of the water).
2. I have only achieved growth in a high nutrient tank. This is the only way I have ever run my tank though. I enjoy feeding both fish and corals. I tend to overdo feeding a little, but I can deal with the results (cyano) since the action is my favorite part of reef keeping.
3. I find that growth of all of my corals seemingly goes in spurts.... I do not see one head grow per week on zoas. I will notice 8 heads one day and then maybe 8 more a couple days later and then not really notice much growth for awhile. I also notice this on other corals. I will notice the growth tips on my birdsnest one week and then the next it just seems to be stopped. What I have witnessed is the period of "non growth" is a period of strengthening of the coral. In the birdsnest's case this means thickening of the branches and main stems. The zoas on the other hand, tend to grow their mat or outwards more during this time. On LPS, like euphyllia (frogspawn) the out ward growth is a little different. There seems to be an upward period where the heads stretch up and are very large. I believe this is when the skeleton is growing. Then they seem to pull up the tissue from the bottom and dont reach nearly as far. After a week or so they puff up big again.... then the pull up...
4. There are many factors that could be an issue with the growth I have noticed. The water change schedule is the major one. The corals may grow when they get the boost from the nutrients in fresh water... then get stunted until the next water change. I am pretty good with my water changes (weekly)... but occasionally miss them (like this week.... ended up being 2 weeks before). I have not been in the hobby long enough to be able to correlate the "mini growth stunts" to a week that I missed a water change.
Along with water changes, I think feeding can be a determining factor of growth. In another thread we talked about single polyp fragging.... I cannot usually get a single polyp to feed. Once it makes it to about 10 heads I find out if I can really get it to feed. I feed any coral that will readily accept meaty foods like mysis. This includes: zoas, palys, lps, and ricordeas.
5. I really have nothing on this one.... I wish I knew more about zoa origin but really have no clue. If someone wants to make a guide I would happily comment on what I have noticed (I have seen the website that lists origins but found that it was lacking in thoroughness).
I voted for high nutrient since this is the zoa thread and this is what I currently run.