I think the important point is: some skills change the internal state of the lemming such that that lemming has a different behaviour from normal walking lemmings: he will carry out X skill at any time if the right circumstances arise. These skills are an important group because the engine needs to (and does) provide information about which permanent skills a given lemming has, so as to avoid hidden information. Whether "permanent skills" is a good or bad name for this group doesn't matter; that just is the name we've adopted.

More importantly, "Permanent skill" has a specific meaning in a Lemmings context, and those are the skills usually considered to fall under it. It's been debated exactly which category Cloner should fall under, but I don't believe permanent has ever been proposed - some proposals have put it in the same category as Walker and Shimmier, while others consider it to defy categorization and be in its own category by itself. I don't recall ever specifically seeing it included with the permanents.

The unambiguous categorizations (current or very-likely-future NL skills only) are:

Movement skill - Walker, Shimmier, Jumper
Permanent skill - Climber, Swimmer, Floater, Glider, Disarmer
Constructive skill - Platformer, Builder, Stacker
Destructive skill - Basher, Fencer, Miner, Digger

Some people would put Bomber and Stoner under destructive / constructive respectively, though it's more common to group the two together under "Fatal skills" or some other term like that. Blocker is sometimes included with these, sometimes included with Movement skills, and sometimes considered unique much like Cloner can be. It has been recognized that the Blocker shares traits with the permanent skills to some extent, though I don't think I've actually seen it considered to be one - such recognition is usually been used more to say "the blocker should be next to the permanent skills on the skill bar".

Of course, this kind of discussion is of limited importance in terms of actual gameplay, as the skill will do the same thing regardless of what category you consider it to fall under. The only time it's had direct relevance to NL is in discussions of how to order the skills on the panel, but so far the only time such consideration has been applied was in deciding where in the order the Fencer and Shimmier should go - the other 8 skills predate much consideration of such, and have just kept the order they were originally assigned (although this does end up quite strongly reflecting the above anyway).

Either is "correct" and will work. Using a subfolder is the recommended approach; but most people ignore this.

You need to include the folder in such cases. For example, specify "Lemmings_Plus_III/bam4" in levels / music.nxmi for "bam4" in the folder "Lemmings_Plus_III".

Thanks for the replays, I see no backroutes here.

Comments:

The O&F 11 & 12 pre-screens specify "(None)" as the hotkey for the various tasks; I'm sure this is something you're aware of and will get around to changing, but just a heads-up anyway.

I have no influence on that one. Which hotkey layout did you choose with the installation? These layouts should cover the hotkeys mentioned here otherwise point these missing ones out to namida, together with the layout you chose.
You can also assign them manually in the hotkey menu.

With the former, since it's not possible to save all the Lemmings it kind of gives the splitter object a bad first impression.

It is possible to save everyone, indeed my replay does so, but a point of the levels is to show the player that loosing lemmings is indeed alright. In this level you can loose a third of the crowd and the player should feel empowered to do so. The save requirement is not 100% for a reason, new players should loose lemmings here.
I can lower the save requirement if you advice, but losses should be expected. Players must learn and get used to let lemmings go.

With levels that introduce a completely new concept or object (pickups, buttons, splitters, teleporters, limited-number entrances & exits), it may be an idea to make them as basic as possible - like, first few levels of Fun basic. Just showing the player what the item does, but not in the context of a puzzle just yet. Or, present the item first in a simple set-up level, and then have a puzzle level straight afterwards (this would obviously increase the number of levels...). Just an idea, and one I'm sure you have already considered. If you were to leave it as is, it's totally fine and perfectly enjoyable for any decent Lemmings player. But if the idea is to welcome in complete beginners, then presenting the new stuff in the same manner as the skills themselves may be worthwhile...

Well, these should be the very basic cases which still cover every aspect mentioned.
For the gravity level for example here is my creation thinking process: I covered all 3 instances of updraft interactions: Normal, floater, glider. The only puzzle should be in which order the 2 permanent skills must be assigned to the 3 lemmings, this is also hinted at inside the pre-text. The 2 builders 100% have to cover the water pit and the splatpad there is no alternative, as otherwise the level is always impossible and not all lemings can go towards the exit. The 1 fencer has to be for the last pillar.

Well, collaboration packs are very hard to get rolling. Let's say most of the time people already have their projects. Packs are a ton of work, I spend over 3 years creating Lemmings United for example, it's quite the commitment.

Also, the timing is quite tricky: Quite a few users still work on updates for styles and packs after the update, others are planning their contest entries.

My golden rule would be: If you want something done really badly, do it yourself and don't wait for others. that's why I converted the L2 sets back in the day, I wanted them in NL so I did them in NL.

I personally have enough projects running and planned for now and if it came to my mind to redo some tame levels I would cherry pick a few where I can imagine an interesting variation.