For 1) Blender cannot do everything itself. . . and sometimes you have to “adjust” some edges / vertex.
In the case of 0 (Zero), adding edges at the top and bottom is perfect.
For 2) Here, for the two overlapping vertices: I select the two vertices> ALT + M> (Merge) At Center
(you can also use the Snap adjust on Vertex)
when I applied Bevel, the manually added top and bottom edges created two lines both on the top surface and the bevel area
It’s normal . . . because by selecting the faces, you ALSO select the edges …
So, you have to go back to selection of edges and deselect these two edges which are problematic
In short, always look at its mesh and make the few corrections that are necessary.