I got a few results for LPII Bonus Pack - mostly only those that are obvious or quite simple to work out.
Trial 1 - There is quite obviously no way to solve this without using every skill, so that answers both challenges.
Challenge 7 - Fairly sure the 4 blocker approach is the only way, which answers both challenges.
Reverse 1 - A two-skill solution is possible with a builder and a miner (doesn't appear to be any one-skill solution). It can also be solved with a blocker, a builder and a digger. The normal solution only uses a miner and a digger. Therefore, the answer for can't live without is
none.
Reverse 2 - Bomber/Blocker/Basher is one combo that works. A slight variant of this swaps the basher for a builder. Another variant can instead swap the bomber for a builder. A different approach can complete the level with two bashers and a bomber (thus eliminating the blocker). So this one is also none.
Flight 1 - I don't have a final result for minimum skills, but for can't live without, see attached replay for solution with no builders. Once you've got that, eliminating bashers is fairly simple, and anything else is completely trivial. EDIT: I cannot find any way to do it with less than 7 skills. My solution to acheive this is a fairly obvious combination of builders and bashers.
Rush 1 - Fewest diggers I can seem to solve it with is 8. RR 97 before the first lemming, then 99 before the next one, and then it's just a matter of leaving every digger as late as possible.
Rush 2 - Good luck solving this with anything short of the full 60 builders.
Rush 3 - Quite obviously 80 floaters, also meaning 80 skills minimum.
Rush 5 - By similar logic, this one is 64 each of climbers and floaters.
Rush 6 - And by similar logic again, 66 bombers here.
EDIT: Also improved a few of the minimum skills for Mild levels in LPDOS:
Mild 5: Reduced to 2 skills (was 3). Replay attached, it's not exactly unobvious but does require careful timing.
Mild 8: Reduced to 1 skill (was 2). It's a glitch solution, but a fairly obvious one, so I didn't upload a replay.
Use the nuke glitch.Mild 15: Reduced to 2 skills (was 3). Replay attached. Like Mild 5, this one is a matter of timing - in fact, the 2-skill solution here is very similar to the one there!
Mild 23: Reduced to 3 skills (was 5). Replay attached. Like Mild 8, this one uses the
nuke glitch; though it also features very tight timing. Attempts to reduce to 2 skills using a similar method have failed; the most I can save with 2 skills is 55% (requirement is 60%).