It would be my opinion to remove the damaged sub-flooring. Any flooring will require a smooth surface before installation, including carpeting. If you don't have that, you will void your warranty AND end up having to redo the floor and sub-floor.
Over time, you'll probably wear the high spots in the carpeting over the damaged sub-floor and may end up noticing the high spots. Do NOT cover over the damaged areas with another layer of sub-flooring. Again, over time, even if you were to be bold and screw and glue the 2nd layer of sub-flooring to the damaged layer, the bottom layer may end up pushing up the new sub-floor, thus, causing problems with whatever you installed over it. Hardwood especially! It's very sensitive to movement underneath.
Set your power saw to the depth of the sub-floor, and use a chalk line to mark the area you want to cut out. Make sure the area(s) you cut out are centered over joists at the ends. You don't want the ends of your new sub-floor 'hanging' between 2 joists! The new sub-floor should be cut in increments of 16". (That will center you over joists installed at 16" on-center (OC). (If your joists are installed 14" OC, then cut your new sub-floor in 14" increments.) AND, to boot, the smallest piece of sub-flooring should span 3 joists; NOT 2! Use construction adhesive and screws for the install. I'd use 3/4" material.
Yes, depending on what you have for sub-flooring and what you install for your flooring, you may need to address door trim and the thresholds between rooms. Do consider this as part of your design. You can buy a jam-saw to cut the trim and molding around door and entryways between rooms. And you'll most likely have to cut any existing doors. (The latter can get tricky if you have only 'general' tools at your disposal.)
If you need more info, post up or e-mail me directly. My best to ya and hope this helps.