Is it possible to create new skills right now? The option seems to be there, but only half there as far as I can tell.
There's an editable list of skills, and you can choose to duplicate, create, or edit them, but certain important options are greyed out, such as the ability to actually set it as a "Skill". Even if you duplicate an existing skill, it seems to remove the "Skill" tag from it.

Exactly the same dilemma I have been facing, It's really starting to make me angry.. I have tried everything, even manually going over the files in Tes-snip, creating the Actor values's in skyedit, everything.. either total crash or no luck...

Is it possible to delete existing skills and their relevant perk trees? I'd be interested in creating just 4 perk trees, with multiple skills being represented by each perk tree, but if that is not possible I'd happily reduce down to 4 skills and work on molding existing skills to my needs.

Most likely the skills and number of skills are hard coded into the game engine.

In earlier games, people made "pseudo-skills" using global variables to keep track of skill value and scripts to keep track of experience and skill increases.

The option in the CK is bugged. All we can do is hope they fix it.

Is it really "bugged" though?

It seems to be implemented this way, which leads me to the conclusion that they don't want/care about us creating/editing skills.

If it was implemented in a way that new skills weren't possible, then they would have removed the new record right click option. Plus according to that "Skyrim Jam" video, someone made a lycanthropy skill and perk tree in a week. For a simple week project that's not something that they would have likely modified the whole engine to add.

(1) They only remove stuff that gets in the way. If they didn't remove the pointless error messages laoding skyrim.esm, they sure didn't have time to remove stuff like this.
(2) They probably created the new tree in place of the completely pointless lockpicking tree. That's what I would do, if I wanted a new perk tree.

They removed 4 broken toolbar buttons left from the CS and the GECK. Look at the YouTube videos of Bethesda's tutorials, they have more buttons than us on the toolbar. However all those buttons would have been broken (new scripting engine, SpeedTree removed, VersionControl, Broken Grid button etc). They removed them in order to slim the interface down.

They don't remove things randomly. If the right click new option is there (and it wasn't in the CS or the GECK), then it's there for a reason. They wouldn't remove that functionality from the retail CK, it would make absolutely no sense to do so. It's a bug.

Something else is off. The Actor Values point to scripts of the same name which are supposed to designate how they work. I was excited as hell when I thought I could change the core functionality of existing skills directly, but the scripts listed don't actually seem to exist. At least, I can't find them listed in the Papyrus Script Manager.