1. 16 teams or 12 teams.
I prefer 16, myself. If we can find 4 signup candidates (start recruiting early - like maybe _now_) who have some degree of verifiable fantasy pedigree I'd rather that. "First four to raise their hands" is probably a risk we don't want to take. And yes, I realize the irony that if you applied a selective process last summer I likely wouldn't be in this league.
I also don't especially like how talentheavy the draft becomes if there's a sudden 4-team dispersal. The formulation of this league was that first round picks next year would exclude approximately the top 16x4=64 top players in the league, who would already be owned. Some teams being better than others, there might be a handful of players in the 30-40 range available (the fifthbest players on the deepest teams) and those would be the plum assets (along with McEichel) available as consolation prize for bottom finishers. With four folds, the draft pool gets seeded with multiple top players like Benn, Tarasenko, Nash, Toews, Quick, Perry, Subban... even the good teams will be getting a massive talent gifted to them in the draft.
2. Goalie appearances 3 or 2.
If teamcount reduces at all, 3. If teamcount stays at 16, 2. This league has easy accumulator stat Saves as a category anyway (rather than win-early-and-sit-on-it Shutouts); sitting after 2 good starts, even shutouts, in this league will often only earn you a 2-2 as the other team can easily outpace you on saves and often outpace you on wins by playing quantity over quality.
3. Offensive stats category. Leave at 8 categories or increase to 10.
8:4 is already a more offensive-weighted ratio than typical. If the league was at the standard 6:4 I'd be in favor of bringing it to the 8:4 we have now, but I don't think we need to go any further (like the proposed 10:4).
The three-birds-with-one-stone solution might be to drop one of GAA or SV% as a category. If we did that we could easily go to minimum-2-starts because with only one of those stats in play there's not enough incentive to sit on two early good starts, because accumulator stats (where people are naturally incentivized to want more starts because more starts will never make the stat worse) would outnumber rate stats (where people are inclined to sit on an early lead because more starts could make the stat worse).
16 players, 2 goalie starts minimum, and one of the goalie rate stats chopped would seem to work together well - higher ratio of forward to goalie stats, no incentive to sit at 2 goalie starts, and otherwise keeping the talent distribution equivalent to present.
4. Roster positions. There will be 2 IR+ slots next season.
Yes. I like IR+ a lot.
5. Keeper rule. Currently it is 4 players.
I think this is a change that needs a year of lead warning. Drafting this summer should be made with an eye to how many of the players you draft you'll be able to keep. When we drafted last summer we kept an eye to keeping 4 players, not 6.
6. Draft Order.
This is another question strongly dependent on "what are we doing if we replace the dropouts"? I would rather we replace the dropouts, have them redistribute their own 'keepers' in a 4-round cross-pollination draft in which they can only draft from among the players on those 4 teams, then start the 'real' draft in which they'd be slotted into the mix of nonplayoff teams, with the player who got the first Benn (sorry, first pick) in the cross-pollination draft getting the latest pick of the four in the full draft.
). We just need to figure out the draft order for next season. Any thoughts?
). Provides for more thought when making lineup decisions if you are down or close in that category to your opponent or even when drafting. 
