Haven't played Dungeon World, but sounds like a nice mechanic for that ruleset. Although, not having the context of having played DW, the description you provide here doesn't sound all that different from playing 5e.
Very much the same as in D&D 5e, in my experience, with the key being the bolded part - and everything else follows.
Again, plays very much the same in 5e at our table. Most any action declaration to make the right puzzle move (or to not make the wrong puzzle move) might be met with a DM asking for an ability check - that is, if the action has the possibility of success or failure, and meaningful consequences for said failure.
Hmm... I guess one might say that the distinction between "skilled play" and "narrative play" needn't have a strongly defined border.