I’m guessing if you plugged both of these into a plastic or wooden case and touched the exposed metal parts that you would not get a shock, so probably safe...but no harm in adding some simple insulation washers anyway just to be sure...even cut from heavy duty plastic bags (freezer bags work well).
The outside of the connectors is electrically connected by the aluminum case,
is this...
Yes they are designed to do this. It is only a problem if you wire things to the ground connectors other than ground, then they will short out. Unless you have over 50V in the circuit there is no risk of electric schocks.
The act of mounting an RF device in a screened box might upset the output impedance matching but it is unlikely.
RF connectors are normally grounded to the case. Audio or sensor signals are more likely to require isolation
to avoid ground-loop noise injection.
You can ground the power input too, unless you have a need for a star-ground system due to sensitive low
voltage signals, but even then you can use the incoming power connector as the star point.