Anything alkaline will work on alkyd/oil in high enough concentration.
However, alkalines can react with tannic acid in some hard woods leaving black spots.
Try a heat gun, or up the pH by using ammonia mixed with wallpaper paste or other thickener
this is especially true for: resin-rich wood (pine, most conifers for example)
But also a distinction is made between constructs that must maintain their dimensions, and those that must not.
I.e. Windows/doors can change dimensions in the heat and no longer fit right in their openings.
Water gets in those joint pretty easily, and the particle/fiber board beneath can expand like a sponge.
Have you tried vinyl "laminate"? It's basically the exact same, just wood-free and thus has no problems with water.
Plus you can cut and snap it with a razor like with drywall.
You should sand first if you want to paint over. This will release lead dust however.
You can also strip lead paint with anything alkaline enough.
Lime plaster mixed with natural soap is supposed to work, I did it recently with ammonia and wallpaper paste. You should only use the ammonia with...
You don't have to de-rust it, but the reason it's popped off is because it has rusted (kind of contradictory, I know)
The reason is, the alkalinity in the cement prevents rebar from rusting any further--provided IS still alkaline (cement neutralizes reacting with CO2 in the air).