How do you store a magnetic base and a dial indicator to prolong their life and retain accuracy?
Storing the mag base "off" is equivalent to storing it "on" attached to a thick ferrous item - "off" is "magnetically attached to itself internally." Either is fine. This serves the same function as a "keeper" bar for a plain permanent magnet. A thin surface (sheet metal) is not as good, and "on" but not attached to anything risks weakening the magnet over time.

Orientation during storage does not matter.

Leaving the dial indicator out is going to vary with local hazards - are you likely to knock into it if it's just sitting there? - Then put it away. Putting it away is standard in a multiperson shop, but your home shop practices can vary with your level of care.