I'm no expert, but I know what's worked for me. So I'm answering these on that premise.
1) I wrap my cuttings with whatever works or is handy. Usually a well-rung out, CLEAN but slightly damp paper towel is what's handy, so that's what I use. This is a 'personal preference' thing, I suggest you try both. I didn't like using sphagnum moss, too complicated and it seems that (while mold doesn't like it,) fungus gnats go bananas over it.
2) I use a soap scrub with toothbrush and 10 parts water to 1 parts bleach mix. After the scrub-down, scrubbing the leaf scars especially and all nooks and crannies really good, I dunk my sticks in the bleach dilution and let sit for about a minute, then pull out and rinse well, then allow to fully air dry. Truth be told, I think the antibacterial soap is baloney, believe me, the bleach solution is going to adequately kill any bacteria on the cutting, the purpose for soap + toothbrush scrubbing is to debride any possible food material from the cutting so mold has nothing to feed on.
3) i know 'Danab' recommended that a good way to get a stubborn cutting to root is to cut around the base near a node. I found this worked on the two that I tried, but I have no evidence to say that it worked for any other reason than it was time for the cutting to come out of its slumber. I argue that every leaf scar is a "wound", so I don't see why it is logical to say that cutting into a branch is nearly as bad as a leaf scar, which is a gaping wound on a cutting (must scrub those very well! Common source for mold to eat!). In my mind, it is illogical to think that a single cut into bark would be even a fraction as bad as a leaf wound, fresh or otherwise. OR any worse than when you need to snap off premature growth or figs from a feisty cutting.
NOTE: Plants in the ficus genus seem to be notorious for having a large number of undifferentiated cells, which can either become root or bark or whatever. So, technically, cutting or notching a plant inspires new cell growth, which with undifferentiated cells, can result in roots forming where once was bark. This is the basic principle behind airlayering, and why airlayering works. Read up on undifferentiated cells in plants for more info.
4) I would never in a million years use vermiculite. Period. Not when rooting. Too fine, holds too much water. If starting in cups, indoors, I could never in a million years fathom using anything less than a 50% coarse perlite mix, although I truthfully like doing more of an 80% perlite, 20% potting mix (NO fertizler inside!!). Don't buy into the hype on potting mixes. Yard dirt will work fine, cuttings don't need any significant nutrients until they've been growing for several months (4-6 months or more).
5) I don't buy into the refrigerator/dormancy hype either. I started 100+ cuttings this last year with the vast majority getting no cold storage. I had about 90% rooting rate in the end, with about 75% survival (lost a lot during 2 weeks in Spain/Italy). Of the ones I put in the fridge, I lost damned near half to rot and other issues. The lack of cold didn't hinder my cuttings from what I can tell, and the refrigerator was more of a death sentence than *I* was!!
6) Don't have an opinion. I cut all of my trees back to whatever point will result in a nice shape, shrubs and plants alike. Well, except for finicky corner case plants like Rosemary or Roses, where you need to cut back to a specific location for best results (or to ensure a plant will live). Figs, like Mulberries, are a weed. No matter where you cut them back to, if the thing still has roots, it's going to grow back. The only way to kill one that's in-ground is to dig the main root ball out of the ground.
7) Always make cuts in a manner that water will not stagnate during or after healing. When the wood hardens and hollows later, you can remove any excess points.
8) I agree, this is personal judgement.
9) You can take cuttings any time, dormancy or not. Most people prefer to take cuttings during dormancy, but others argue that trees are more apt to grow quickly when the tree is vigorously growing. Again, the concept of airlayering is pretty solid proof of this - vigorous rooting when the tree is actively growing. I wouldn't buy into the dormancy hype here either.
10) See #9
11) I don't know what triggers awakening in figs, but with many plants, it's a combination of soil temperature and ambient temperature, with soil temp being the big motivator.