Don't leave the robot in the water for any longer than needed. Sometimes you have no choice but the manufacturers want them removed as soon as possible.
The only exception I know of is the Dolphin Explorer.
Sunlight is ok, although it will yellow any white plastic. Don't cover the robot, condensation may occur.
A shed works great for storage so long as the robot is kept away from pool chemicals.
Wet chlorine is not only a fire hazard but it will corrode metal and destroy fabric that may be in the shed as well.
Store the robot indoors during the winter ONLY if it may be frozen.
The Nastybag is a quality stitched microfabric as is the Wonderbag. I have used them both. Seems the only difference is Nastybag is sold as a liner and Wonderbag is sold as a replacement bag. I use Nastybag as a replacement bag. I get at least two , sometimes more, cleaning cycles per bag and the convenience is worth every penny.
One admonishment. do NOT plug in the robot unless it is in the water. Plug it in after it goes in, unplug before it comes out. Running the robot dry will damage it.