Taxing: No results yet
Well, I have results to report now for Taxing 1-10. I would've reported at least 2 hours sooner if I could just post Lemmix replays instead of having to make screenshots and all that nonsense.
Here are the levels that I found impossible:
Taxing 2: I fail to find any way to get across the water fast enough to prevent too many lemmings being lost on the other side of the water.
Taxing 7: when your worker finishes all the building to the exit, there're not enough skills left for your worker to go back to release the crowd.
Taxing 9: you don't have enough skills to get a deep enough pit fast enough to trap the 2nd lemming out. Trying to quickly build right for a survivable drop also doesn't work (you can't make it fast enough for the 2nd lemming out).
Here are the levels that I found possible but non-100%:
Taxing 5: similar to Taxing 9, there're not enough skills to get a deep enough pit fast enough to trap the 2nd lemming out. But it's possible to lose no lemmings other than that one.
Taxing 6: The only known 100% solution requires bashing through the top portion of steel on the right, which is only possible if you are no more than 5 pixels down from ground level. But to prevent lemmings from falling off on the left, you have to dig down at least 7 pixels from ground level. And there's just no way to go from 7 pixels to 5 pixels with the skills given and the constraints of the challenge. My best so far is lose 5.
So in summary: 1,3-6,8,10; non-100%: 5,6
I've attached two zip files. One contains only Lemmix replays. The other contains screenshots and some text notes as well, for those who can't/won't use Lemmix.