Re: re water flappers
The metal bar going across the center of the exhaust pipe is the remnants of your old exhaust shutter. The shutters are in there to prevent the exhaust manifold and engine from flooding in the event you take a wave across the stern or abruptly stop the boat,,, which will swamp the exhaust. Soooo, yes it needs to be replaced.
If the old one is riveted in there you will need to drill out the rivets and then screw/nut the new one back on. Don't loose the brackets that hold the shutter as you will reuse them when installing the new shutters. I would also lock-tite the nuts to make sure they don't come loose.
Now you have to ask yourself what caused the shutters to burn out, lack of water flow, running the engine without water, old age?