You cannot select disconnected net branches using the conext menu option, to select all segments you should select the net in the Navigator. Depending on the version of the software you are using you can switch the nets on and off in the navigator using the Display Control (View - Display Control). Similarly you cannot select a net if you have symbol selected (your second use case).
You may want to vote for this idea Triple click to select entire net with all segments - D3241
Selecting the net in the navigator is a waste of time if we need to verify smething in the schematic.
Before migrating to PADS VX, we used PADS V9.2 (Logic) and it was very useful to select all part of the net.
The idea has 8 years so is Mentor planning to implement this feature or not?
Thanks for reply.