Deleting non-manifold Edges?

This mesh has a number of problems, including non-manifold Edges. I can Select them using SELECT BY TRAIT, but when I use DELETE or DISSOLVE EDGES, it messes up the mesh.

What is the proper method to kill these bad Edges? Tnx.
NONmanifold.blend (600.7 KB)

You can fix some problems by “merge by distance” and check on “merge” for the mirror modifier.
But as far as i see the mesh does not suit well for subdivision modifier yet. But i am still a retopo noob so maybe anotherone can tell more here.