That damage on the bottom is odd.....guess would be, they're not cooking but using for a fire pit, probably a bunch of times......
"What else should I be doing with the lid and bowl?"
Couple things come to mind....
As it's already been painted, maybe, I say maybe, go for a careful grind down, priming & painting........... Wouldn't be a perfect "Restore" adherent, but probably would last longer / work better.........
There is several products that will stop the rust within the crazing dead ( POR 15 is one )
The rust would be good to stop if at all possible......
Ash pan, now that I got a close look at one, could be matched with a very small wok, painted hi-heat silver to prevent rust or a medium chrome mixing bowl.......
" - square it up. Any suggestions on how to approach that are most welcome!"
The one I just got, the current owner had never fired it up, but he did add some small metal angle / corner braces in fairly inconspicuous places to square & shore it from wobble.................
I can send pics of what he did & it seems really stable, so those I'm leaving in or reinstalling after finishing.....
I'll add whatever info I can to help with the wood part, it's where I'm headed !!!
Forgot to add.....the wood still really looks in pretty good shape.....
your wheels look great & at least the doors are still there.....not sure what happened to mine?
maybe they just plain didn't like them ......