Ratskinner
Adventurer
The most developed non-combat resolution system for D&D that I'm aware of is the skill challenge in 4e. It needs your (a) but no rulebook directly states it. A GM needs either to bring that from outside (normally by experience with another game with better-stated rules), or intuit it, or else complain that skill challenges are broken because we have to keep rolling the dice even though the conflict is resolved!
I agree, although I think the Skill Challenge was a bit clunky overall.
I'm not sure about your (1). In 4e the standard solution is to just ignore all the quasi-simulationist stuff in the PHB skills chapter (which is mostly dropped in Essentials, for good reason). I'm not sure that 5e skills are really even quasi-simulatoinist, though I'm not the best qualified to comment. I think the issue is less about quasi-simulation and more about setting appropriate expectations for players and GMs: eg having a good Investigation skill means (something like) when a conflict involves investigating stuff, than I'm more likely to succeed at that conflict than others. This will cause a lot of players to go ballistic but for culture/expectation reasons rather than narrowly mechanical reasons.
I think my problem here is that after a game like Capes, its really hard to fuzz my eyes as much as I used to. Capes doesn't even have skills. You just have traits. The traits can be almost anything: "Hit 'em with the scenery", "Do a dozen things at the same time." (remember its a supers game) So, when its a character's turn, the controlling player just picks one and narrates a relevant bit of story (there's some complicated dice/point manipulation stuff, too). Thing is, your ratings in the abilities don't correspond to any sort of "power level" or "ability level". So one character might have "Interplanetary Flight" at 1 and another has "Angel Wings" at 5. The wings are "objectively" less powerful in the narrative context, but in a game where "Impress Allison" can be a goal, the wings will be more useful. The trait ratings end up being solely a rough measure of how much you want a given trait to matter in this character's story.
Your (2) is a recurring issue in 4e play, although most of us who care have developed various sorts of workarounds/coping mechanisms. It's an issue even in a system that one might expect to be tighter than 4e, like BW:
I think the best I've seen is the Forged in the Dark games (based of Blades in the Dark). There's good discussions in those games about "clocks", which to my eyes are very similar if not the same as Conflict Resolution (I think there's some wiggle room, depending on how the GM runs a given clock). Its not the most sophisticated discussion ever, but they do discuss things like contingent or sequential clocks. Of course, they have the advantage of a system that uses the same resolution mechanics for all conflicts (at least during the mission/adventure/heist). In Capes, creating conflicting Conflicts is just a way for the players to manipulate the "not yet" rule. (At the player level, Capes is competitive and GMless.)