When it comes to dry-firing, it's not typically a good idea to do it with most .22 firearms. The reason being, is that the firing pin (steel) can hit the steel edge of the chamber. Steel against steel (with no brass to buffer the blow) = no good. It can potentially damage the firing pin or the chamber rim.

As far as storage, I wouldn't store it with a .22lr case in it. An empty bore and chamber is typically the best way to store a firearm, that way you can always ensure it's unloaded with a quick check of the chamber. Leaving a shell in there might cause you to confuse an empty shell for a loaded cartridge, thereby potentially leading to a dangerous negligent discharge.

Now, on a lot of .22's you can pull the bolt all the way back and then (ensuring the gun is empty), at the same time, pull and hold the trigger while slowly letting the bolt forward. This then allows the firearm to be stored un-cocked. I forget whether or not the 795 can do this, but if it can, that's the best way to store it.

Otherwise, if it doesn't let you un-cock it, I would store it cocked on an empty chamber. Most people prefer not to store firearms cocked, as it can potentially wear springs. However, the act of shooting the firearm puts more wear on the springs than leaving them compressed does, so it really isn't a big deal.