How Does Synthesis Support Effect Skilling Up?

Does the support buff mean what you craft is considering your craft level + the buff as your crafting level or does the synthesis support just give you a better chance of success while still maintaining the skill up chance of your base crafting level?

In other words, if I get advanced support will I stop skilling up when my crafting level reaches 3 levels below the cap for the recipe?

crafting skill ups
I'd read it as your skill enhancements, regardless if from gear, synth support or furniture, don't affect skill gain rate if you'd "overcap" due to +skill. However you're on the safe side if you start removing enhancement equipment and synth support once you're nearing +11 skill over cap, unless you're trying for some lucky HQs while skilling up.

I'm not sure what the sentence about "must be either less than the synth's level cap,...". Afaik they changed skill ups at some point so if a skill would cap at level 90 you can still gain skill ups till you hit level 101.0, although probably at a lower rate. So the "cap" level you can find on bgwiki is only correct (probably also not always) for HQ rate calcualations, for "crafting skill up cap" you need to add 11 skill on top.

IIRC you can however start skilling up sooner on higher lvl synths when your +skill brings you in range of the new recipe, I think roughly within 10 levels better 6.

No, effects and gear does not impact ability to skill up

I'm pretty sure 7 is the magic number; you can attempt the synth with a larger gap (I want to say 11 levels? EDIT: Wow, way off. 27 apparently, but by 11 I've found you're already in "may as well just throw it away" fail rates) but 8 or more won't give skillups on a break, 7 or less can.