But the mechanism is the same, and Darwin proposed it to be the same. The phenomenon of inheritance was well known and well established, and it was the mechanism Darwin proposed to explain evolution. Had he been aware of Mendel's work, he likely would have recognized it as the underlying principle of inheritance - Mendel did. In fact, Mendel's own copy of "Origin" has his notes in the margin indicating his understanding of how his work in genetics supported Darwin's work on evolution.
Well, that's precisely the point at issue.
No. You don't have to understand advanced aerodynamics to propose that a duck flies by the same mechanism as a goose. Darwin didn't have to understand DNA to propose that inheritance from species to species operates by the same general mechanism as inheritance from parent to child.
Mendel did not own a copy of Origin.
His monastery did own a copy and there is some underlining in that copy, but no verbal notes.
It is certainly possible that Mendel was the underliner.