The part on the floor of the cuddy that the very base of the mast, or mast stub in your hinged case, sits on is called the step. The foredeck would be the top area forward of the cuddy roof. More pesky terminology! Just make sure that when you reinstall the stub, you secure it to the step in some fashion, or else the stub will want to lift when you step (raise/lower) the mast. Yes, step has two different meanings here.
You are correct that the hinged spreaders are for the side stays, or shrouds, and you will want to use some thin wire or the like to secure the shrouds to the spreaders, then use spreader boots or some tape to cover the spreader ends to prevent chafing the main sail. The other spreaders and associated cord sound like jumper stays, which were found on the early DS's, and which most folks removed in order to get more, not less, flexibility at the top of the mast. Either your boat has a mast from a much earlier boat, or some PO added these to try to fix the bend. I suspect the latter, and I think most here would advise removal. Like you say, you'll need to remove them anyway to effect mast straightening.
Mast head replacement is fairly straightforward, with the earlier rivet removal advice applying here as well. Or, you might be able to just replace the sheaves. Either way, yes, floatation near the mast top is desirable, and you may find there is already foam in there (my boat did). You could easily add to or replace with pool noodle pieces or what have you. There are also external masthead flotation options, such as empty, sealed soda bottles, etc. I made a foam float that fit around the head of the main. Even if whatever you end up with as flotation wouldn't completely prevent turtling in a capsize, at least it buys you time to swim a throwable or similar out to the end of the mast before she goes completely upside down. And yes, intentional capsize drills are a good thing! Especially with kids aboard. Oh, and that reminds me: these boats have foam floatation up in the bow and under the seats, which can (and usually does) become waterlogged over time. Most folks replace the foam with pool noodles or soda bottles. There have been reports of funny looks from big box store cashiers when folks walk up with 40+ noodles in their arms! <grin>