Will the surface beneith the ledge be level with the wall above?

No. It will be level with the wall below

Im attaching more pictures of the dining room. Advice needed on how to paint these walls and the ledge once the paneling in removed. Room has simple cherry colored bookshelves, table and chairs. I'm hesitant to paint the ledge white as with children living here it will probably need constant cleaning. Would staining be better?

Please advise.

I'm not a decorator nor do I play one anywhere, but I think that no matter what you do with it, the "ledge" is going to look kind of odd without the paneling there. Right now it seems to think it's a chair rail.

I can't really tell from the unfortunately dark photos -- is that real paneling? Or is it just plywood? If it's the real thing, I suggest care when you remove it. I'll bet you can find a buyer for it, someone who's restoring a room that's had its original paneling stripped out. Like maybe someone else will do with your room someday. :-\

Would you consider doing a traditional painted wainscot there instead of just drywall? I know you're trying to get rid of paneling, but it's a look that works with the ledge (like David says, treat it like a chair rail). Your furniture looks like it would be happy with the more formal look. Use a good paint and it'll clean okay.

The paneling is being removed due to excessive damage and cracking. There is cinder block behind it (on the outer wall of house, so there will still need to be a 3" ledge and the bottom half of the wall will be 3 inch deeper than top half. I know its kind of odd, but that's what we gotta deal with. Just trying to make it look as beautiful as possible.

I chose Elmira White HC-84 for color of walls. The ledge will be wood, should I do painted white, or stained wood?

Thank you!