You cannot select mirrored edges. To be able to do anything to the mirrored side, you must apply the modifier first, then go back to edit mode.
In 2.79 and before, the "On-clipping" function was not available, but in 2.80+, it allows you to select the mirrored side. It doesn't allow much editing though.
you probably did press E and then Esc. That always results in duplicate vertices. If you dont undo that step and just carry on, you will be left with duplicate vertices in your final mesh, which will always break subsurf (will make a hard edge with lots and lots of duplicate vertices)
To fix it select everything and press Alt+M and select "by Distance".