What could be the reason for the 2 white wires on the right center side of the box? One connects directly to the Neutral bar.
Does there appear to be room to add a 240 breaker to this box? I want to provide for an electric vehicle charging station.
As other comments have stated, it is likely an AFCI or (more likely) a GFCI breaker. Can you determine where that circuit goes? Knowing its termination would help, since some areas, like bathrooms and laundry rooms, are more likely to validate that. Also, it's hard to tell from the picture, but the two white wires shouldn't be connected to each other at the screw terminal. If they are connected, I'm at a loss for what it could be, but if they aren't, then it's some sort of fault protection breaker. I'm a bit surprised by the lack of a test button, though.
It doesn't appear that you have room for a 2-pole breaker to provide 240V for an EV charger. You would need to see the blades on both busbars to indicate room for a 2-pole breaker. In the below image, the red circle shows a blade for the left leg busbar. This is visible in your panel. You would also need the blue circle (right leg busbar) to be exposed.
I know you didn't ask about this, but it seems like it might be a good time for a panel upgrade. You've got five 15A breakers, two 50A breakers, and five 20A breakers for branch circuits all on (what appear to be) tandem circuit breakers, but only a 100A main breaker, which is even taking up space because it's on the busbars directly instead of connected to a lug.
You might want to consider checking if you can upgrade to a larger panel, physically and electrically. Especially for EV charging, which can be a 30A or greater continuous load, you'll probably want to see about 160A service or higher. Depending on the size of the aluminum service entry wires (I can't see what size they are from the picture), you might not even need to replace those.
Something like a 16-slot, 160A (minimum on both) main breaker panel would help you future-proof your panel a bit, especially for adding EV charging capacity. Also, I was able to find a 20-slot, 200A panel with included circuit and main breakers for $150, so it won't likely cost you too much either.