No external power backup is needed for flash memory cards like TF or SD cards.
I can't give an accurate answer about corrosion and oxidation because it depends on the environment. If the board is coated with a monolithic coating or varnish, that will greatly help protect it.
If its in a damp location next to the ocean, it's not going to last long before corrosion sets in.
Best advice is to just store it in a sealed static free bag and store it in a dry and preferably cool location.
The board may outlive both of us.