Ascent does not differentiate between lap markers inserted during a ride, and those you insert later. Both should be deletable.
This is working for me -- are you sure you have the lap selected in the browser before invoking the "Remove Lap Marker" command in the Edit Menu? When the lap is selected, it should be highlighted in the other views of the main browser (map, profile, splits)
If still no joy, please select the activity, right (or control) click, and use the "Email..." feature to send the activity to email@example.com
In the mean time, there's another way to delete lap markers: bring up the Activity Detail window for the activity, click somewhere to front of the lap marker to position the yellow ball, and use the popup menu (right or control-click) to remove the next lap marker.
Regarding the auto-split feature not working -- can you please email an activity where it failed to work, and include the value you have the threshold set to in the email message?