Only one image shows...I would leave as is and paint.

You really should have a deeper door frame to make it perfect. But I have seen many that aren't perfect, so just paint it.

Upon further reflection, I don't think that moulding goes with the rest of the wood. You are going to have a shelf look on the top. Do you want that? Or perhaps it is just the photo. So hard to make decisions based on photos.

looks great as is to me! prob looks weird to you right now, but once all painted, will look fine :)
i think it adds a little character the way it sticks out.

Yes, i do want a little shelf, going to have them put a ridge for little black boards for names with hooks for towels. Hallway is entered from the lake. I may put a piece of wood under the cap on top of the paneling to make it look more substantial.
What about the end at stairs? paneling to end to protect corner or leave it ending at doorway on other side?

that's a tough call.....can you show a pic that shows more of the stairs?

maybe go around the bend a bit like pic shows?

Thanks! Here are the stairs

Returned corner.

As noted above the corner should return to the door casing, not just have a blunt cut.