Use a razor scraper on the drip pan if it is porcelain coated steel (I have an older grill that’s what I use on mine) then steel wool if you want it perfect.
Steel wool and or a brass brush for the burner tubes. You can use water just dry them out good before reuse. Pay special attention to cleaning the holes where the flames come out, brush perpendicular to the rods. Get the holes really perfect.
Yes replace those flavorizers.
I highly recommend solid stainless rod grates. The coated cast iron flakes. The solid stainless rod grates are indestructible and do not rust. Look into the CharGon grate cleaner for those. I think you can get quilmetal 9mm grates for that grill, a little bit of money but your cooks will be ten times better than where you ended up now with fish screens
A good cleaning and attention to detail, new grates and flavorizers bars and you will be amazed! Above all, have fun! I do not envy the project you have around the grill, our house is newer at 1928 but it’s still closing in on a hundred years old so I feel your pain!