Propane shut off

For pure safety sake it is likely better if you do. But I never did.

The danger of leaving it on is two fold
If you brush against a knob on the range you end up with an RV full of Propane and a tank that's empty come spring (Those are the dangers)
If the air/propane mix hits the magic number and there is a spark. the storage facility and all inside it may well cease to exist.. Windows will be shattered for quite some distance, and guess who pays for all this.

Off for me while in storage. These RV systems are not as reliable as your home natural gas.

My gas valve was turned off when the tank is being filled. other wise it is open. 20 years.

If it's not being used, turn it off. In case of a leak.

YES....

Why have a pressurized system when RV is unattended

Yes LP System is only 11"WC *0.39 psi) AFTER the reg but upstream pressure can be 100-250 psi
Close the Vapor/Service valve when 'winterizing'

Simple.........

Why? I never have, and it’s not something I’ve ever heard is necessary.

absotively, posilutely.

No need for pressurized propane lines when in storage.

yes