I agree with all of your points. I'm thinking of including the following distinctions:
1) Aware vs. Unaware (whether they know they are in a dream or not). Being aware will certainly give you substantial modifiers to whatever skill/mechanic we decide to go with as far as manipulating the Dreamscape
2) Dreamer vs. Interloper: If it is your dream, you certainly should have some advantages.
3) Trained vs. Untrained: Ranks in Lucid Dreaming (or whatever we go with) should of course give you advantages and perhaps make things possible which aren't for the untrained dreamer or interloper.
I think an Aware Dreamer should be approximately equal to an Aware Interloper in power, on average, with more highly skilled Interlopers being able to outclass an average Aware Dreamer, but less skilled ones being in real danger if the Dreamer suddenly understands that they are in a dream, and that it has been invaded by someone else, especially if the Dreamer is someone with a powerful mind (not sure how to represent this, maybe a mental ability score check?).
I'm thinking much of this is going to be based on skill use, but what the person can do in the waking world should certainly be accessible to them inside the dream in some form, regardless of whether they're trained, aware, a dreamer, or interloper. I'm thinking that perhaps doing anything beyond the totally mundane (like walking around) will require some kind of a check (probably Lucid Dreaming) which can also be attempted untrained. Being Aware will give a bonus, being the Dreamer will also give a bonus. And I think Skill Tricks and feats as ways to enhance what you can do with the skill are a great idea. That's probably how most of the mechanics I have in mind are going to flesh out.