You can glue the small areas of the rubbber surround back onto the basket using any type of glue that will stick to metal and rubber.
Cut the wires near the solder tags on the speakers, leaving 2mm of the colored insulation. This will give you a reference for re-mounting.
The "magnets" inside the coils are merely ferrite cores (and not magnets).
They merely need to sit inside the coils, so any type of glue able to hold them there will do.
Hot glue is easy and fast.
Martin