Those are pretty rough looking. I've used Oxalic (sp) acid to get rust off of some parts (a search should pull up lots of discussions), but nothing that extreme. Being that this is a classic and vintage forum, maybe you want original parts as much as possible, so if someone else thinks it's possible, it may be worth the effort, but I'd be concerned about performance and safety. In my limited experience, those old, steel rims are hard to true if they get bent, and if those spokes are rusty too, they may not hold up well. With my bike, the first thing I'm working on is a new set of wheels for strength, weight savings, ability to true, and for a machined braking surface. I see you have a rear coaster brake (as do I), maybe the quality of the rear tire has less of an impact on braking, but on my bike at least, my front tire was too dinged to true properly, leaving me an inability to adjust the front brakes well and poor stopping. It was supposed to be the first component to be replaced until I ruined the rear tire...
Now it should be the 2nd thing to be replaced.
It seems like straight, clean (if you're using rim brakes) wheels are one of the biggest factors in a smooth ride, so I'd want to make sure your original tires fit the bill before you put too much effort into them.
Don't worry about gouging the steel as the rust has already pitted it. If the rims are a common size you probably be better off just replacing them. Alloy rims will drastically out-perform steel ones so unless the chrome look is important, you might consider getting new wheels built on the old hubs or just find a set of wheels in better shape. If you do want to use the current rims - and they are solid enough to be safe - a wire brush will remove most of the rust. Then naval jelly or oxalic acid (use search function) will get the rest. However, the chrome will be shot and the metal pitted. No cure for that except to replate the rims. Also, the rims will start to rust again unless they are somehow coated.
Much of the charm of old bikes comes from the patina they collect over the years. However, I think this bike needs a new set of rims. Good luck with the restoration.
Much too far gone. Good for the hubs though, if they are salvageable.
This said, if you can find a somewhat rusty, newer balloon tire (assuming these are 26") job on your local Craigslist with decent wheels, buy it, swap the wheels, then re-sell the slightly "rustier" machine for cheap. Can't hurt.