Are those skylights or fluorescent lights in the kitchen ceiling? Is it grasscloth wallcovering? Yes. You definitely have your work cut out for you. You're just going to have to get all the paper off, fill in where chunks of the wall have been removed/damaged, sand, and probably prime. I think that--even though it's a huge, very un-fun job--great benefits are to be had if you take the time to do an impeccable prep job before you paint. At the very, very least, get the paper off of things that are not walls (like the columns you mentioned). I just have never seen a good paint-over-wallpaper outcome. Sorry.

Since it has been painted over you will probably need to score the wallpaper so the solution can soak in. Scoring tools can be purchased at Lowes or your local paint store. DO NOT over saturate the wallpaper. You can damage the outside paper of the sheetrock. My sister-in-law swears by a solution of hot water and liquid fabric softener. As you are removing the wallpaper be careful not to gouge the sheetrock. When you have removed all of the wallpaper, clean the wall thoroughly, again being careful not to soak the sheetrock. You will probably want to apply a texture to the wall. Prime, then paint. It will probably be cheaper and faster to hire someone to do the texture. :)

BOSTON INTERIORS, so guessing of course that you live near one. My closet one is Mashpee, and I have shopped there many times. Fabric choices are pretty good, so I am sure the designer there could come up with something better to go with your yellow walls, green and orange accents. Just don't let them get too matchy/matchy with their stuff.

HomeDepot and Lowes have limited selections, but if you hit something similar, the prices cannot be beat. Color your World (if still in business) but as soon as you order vs finding a paper in the store, the prices are higher. There are lots of on line companies and my sister purchased hers this way and saved 1/2 the price. It if were me, I would stencil (not very hard - if I can do it, anyone can) and this pattern will be really easy to find - then you have a wider range of colors + save a ton of money. Plus, it can't be damaged like wallpaper can and for a child's room, it's an important aspect to consider. All the best.