Note: All of this is considered hypothetical and in some cases few people believe it at all.
Directions: This is the one that is highly debated and a lot of people dont believe. Facing the direction that corresponds to the element of the crystal you're using will slightly increase your level. Facing 45 degrees to the left i.e. S then move to SW will lower your level slightly. Basically the theory is if you face the directoin that element is weak to then it will increase your HQ rate as well as up the break rate. I usually do it just for skillups, but mostly just because, I really don't buy it, but then again it really doesn't change anything.
Days: Darksday and the Day your crystal is weak to are the best days for HQ's, again theoretically. They also have the most breaks. Lightsday and the same day as your crystal, and perhaps the day its strong to (unsure on that one) are the best days for successful synths. Again, darks and weak to day slightly lower your level, lights and such sightly raise it.
One theory is that there's a zone in there where skillups are highest, the 4-5 levels under the cap of the current synth range. Supposedly this has a higher rate for skillups while not losing your butt off in breaks. I've tried this and it
seems to be true. However its entirely possible that its all placebo effect since I haven't parsed all my skillup synths to see if there's any truth to the matter.
Regular synth enhancement gives you +1 skill, advanced gives you +2 until you become a veteran in your craft, then its +3.
You won't get a skillup on a broken synth until you are no more than 5 lvls below the cap for that synth.
HQ's go in tiers. Tier 0 is <11 levels above the cap and have an estimated hq rate of 1%.
Tier 1 is 11-30 levels above the cap and has an estimated hq rate of anywhere from 10-15% depending on who you talk to.
Tier 2 is 31-50 levels above cap and has an estimated hq rate of 25%
Tier 3 is 51+ and has an estimated hq rate of 50%.
Tier 1 is tricky as it seems to be different with different synths, but all in all you'll get around a 12.5% hq rate when strectched over a large enough base.
You'll also hear of people who get two hq's in a row on a tier 0 synth or people that go 150+ synths and dont get any hq's. There is a certain element of luck involved, but probably if you parsed every crafter in the game it would still probably even out to the above percentages.
Guild point items that add plus skill, which include the body piece, the second equipable piece, the furnishing guild point item, and synth imagery all add to whatever level you're at to determine the tier. I'm assuming at lvl 100 if your a NIN with the cooking katana then you could get to level of 107 rather than every other craft which can only go to 106.
Oh and people have thought that ele staves and bar spells also add to HQ rate. Ofcourse people also thought the sun orbited the earth, so you can just blow that off as nonsense.
For some pretty interesting research and crafting info, check
www.theorderls.com They have a good crafting section and lost of good info, if you can wade through the pages upon pages of flames. Also if you do start looking there, then DO NOT post those question on there. They will flame you endlessly for it. There's nothing wrong with asking those questions, but they're something of elitists for the most part and expect that if you post on there, then you have checked all the available data thus far accumulated and will flame if you if they consider what you asked to be common knowledge....Just a forewarning.