I'm a little busy today and will post results later this week (besides, for some levels I just saved one lemming even though you can clearly do better, so there's still plenty work left result-wise).
Okay, here are my best results so far:
1: 60
2: 60
3: 14
4: 60
5: 60
6: 60
7: 60
(*?)8: 1, 60*
9: 1, 60*
10: 5
Outdoor 8 and 9 uses crawling to save everyone. For Outdoor 9 no-glitch, if builder able to get through the 4-pixel-thick platform is no-glitch, then I suspect the result should be 10, but I haven't bothered with that, so I just put the "1" result I had earlier this week for that level for now.
Outdoor 7 and 10 uses flinging physics. In doing so we'd need to debate what aspects of it may be considered a glitch or not. My current decision is as follows:
A) Flinging effectively "resetting" the fall distance of falling lemmings is not a glitch. I feel this is same as a trampoline doing the same thing, or that you can assign floaters at the last moment and still have the lemming survive. In a way, the main reason it feels strange in real-world physics (not that the game mechanis is all that realistic to start with) is because in real-world physics, most objects takes some time to reach terminal velocity, and that velocity is usually quite high. This is of course completely opposite to how lemmings are depicted falling in the game.
B) Flinging drowning lemmings out of water (so they no longer drown) is not a glitch (although not featured in either Outdoor 7 or 10). The game makes it clear that a drowning lemming is not certain doom until it truly goes underwater (and the lemmings counter goes down by 1). In particular, the game actually forces you to assign skills like kayaker and surfer while the lemming is drowning. So the fact that a lemming can go from drowning to not drowning is completely normal in Lemmings 2, so a fling having this ability is simply a logical outcome.
C) Flinging splatting lemmings, making them no longer splatting from fatal fall, is something I haven't decided yet whether is glitch or not. Unlike the water case, the splatting case feels more like damage is being inflicted immediately, so it feels strange that a fling can somehow undo all that damage. Indeed, the splat animation takes long enough that, you can create cases where you can hardly make out the lemming anymore visually, yet a fling will instantly undo all that disintegration, making it look like the lemming just reappears out of nowhere.
Outdoor 7 in particular, I find it not possible to avoid flinging splatting lemmings in order to save everyone. You should still be able to save plenty though even if you discount the splatting ones. Outdoor 10 barely works (as the attached screenshots show) without having to fling a splatting lemming. If the whole idea of using fling to reset fall distance is not okay for you, then the results for Outdoor 7 and 10 would be 22 and 4.
My Outdoor 9 solution is basically adapted directly from my "6 skills for gold" solution posted a while back in one of the other L2 challenge threads. So aside from the one screenshot depicting the undamaged solution, the rest are just screenshots from that old solution, and they depict exactly how to rope and shoot the arrow.
More details below:
Remember that with 2 lemmings close together, only 1 will be eaten by the frog allowing the other one to pass. You can have a lemming flamethrow at nothing to put it close to the next lemming behind, and similarly with the platformer you have to assign before reaching the frog. And of course the 2 jumpers and 1 hang glider each allows a lemming to pass the frog. So a total of 14 lemmings.
The screenshots basically explain most of it. To get a lemming out of the attractor's reach, just keep jumping him. Later when releasing the crowd, first jump the attractor (who's now ahead of everyone), then jump him at the location with the low ceiling to make him go "oww" (and now behind everyone), then finally jump him while about halfway down the slope to merge him in with the crowd.
The reason you can't just fire the bazooka earlier to avoid flinging splatting lemmings, is because some of the lemmings higher in the fall, will get flung into overhead terrain and fail to make it to where we want them to go. If you look at screenshot H you can see how close some of the lemmings are to getting snagged by terrain overhead.
First lemming make it runner, and he will eventually make it to the bottom of the level where he can platform over the gap. Second lemming can hop to get to where we want it to be as depicted in screenshot A. He then jump left to reach the steel structure with the water, and then bomb to fling 2 falling lemmings to safety. The screenshots depict how close one of the lemming is to hitting ground before the flinging occurs. If we bomb earlier, then the other lemming is too high to feel the explosion and won't get flung.
Finally, save one more lemming using the remaining platformer and jumper, as depicted in screenshot D.
It shouldn't be hard to work out how to save 4 lemmings if you are not allowed to use flinging to reset fall distances.
