I would guess that both problems are down to primers. A primer is, in a way, the most important of the paint layers.
If you're down to bare concrete over all of the sill, I'd go for a masonry paint such as Weathershield. If you still have old gloss on the sill, then you might be better off going with gloss again. Prime the bare sections with a good primer/sealer, or even a strong Water:PVA mix.
Same for the rads really. Loads of people have no trouble with ordinary gloss on a rad. Rub down with a wire wheel on a drill........... to bare metal. Use a universal, or a good metal primer......... then u/c and gloss.



