So, this is more or or less stream of consciousness notes, the first thing that comes to mind when reading this thread. I'll go over to the Wiki later.

No skill points based on intelligence is a really new approach to me, and not one I've ever seen before. My first instinct is to cling to the fluff and say "But smart people learn more!" but we'll see where this goes. Your reasoning seems basically solid.
An interesting side effect of that is that intelligence is now a "useless" attribute. It is, together with Charisma, the only attribute that doesn't seem to influence anything other than skill modifiers, outside of classes. Strength has breaking down doors and carrying capacity. Dexterity is AC and reflexes. Constitution is HP and fortitude and Wisdom is will saves. Pure int and cha are... nothing. THat said, the replacement save thing might save this.

Cross class ranks: I think most house rule collections I've seen do this now. It just makes sense.

Retraining: this is something I never liked. "Oh, no. Redgar can't climb anymore. He learned swimming this morning." It's... silly. Yes, I see the benefit of flexibility. And I dislike it.

All boni are competence boni: why? I'd at least leave circumstance boni in. They make sense. A task is easier for some reason, so you have a +2. It's one of the DMs most important tools for players with creative planning.

Skills unlock new abilities: no problems with that. Good thing. At least you didn't include Skill tricks, I hate them.

Degrees of success are theoretically a good idea. I'm just wondering how complicated this system is now getting. Have you ever seen it in actual play?

I'm not sure I like the "Taking 20 includes having rolled a 1" rule. Taking twenty usually represents being much, much more careful. I don't see "automatic failure first" working with this. "I'm taking this trap apart part by part with my finest tool and the plans open on my lap so nothing can go wrong!" -> Bang automatic failure, you die. This just doesn't seem right. Taking 20 is to avoid failures, not producing them.

Knowledge skills. This, I think, is the first change that makes me go "nononono" in my head. That would never happen at my table. Knowledge skills are essential to the game. I don't want them handwaved. You say they depend on the type of campaign. So does every other skill. If you never need to know history, knowledge: history is useless. If you never get punched while spellcasting, concentration is just as useless. If we exclude every skill that could ever be useless, there would be nothing left.

Also perform. It's an essential skill, and I wouldn't want it removed. Half my characters are either bards or practised performers, and I can think of a dozen anecdotes off-hand where a player's performance saved a campaign in some way. Same with knowledge. Walking on air comes up very rarely. Where it does, I'd probably just allow a player to do it for show (i.e. write it on their character sheet).

I'll get to specific skill examples later.