Hi Ensign Crow and welcome to the community.
1- There are no indicators that Im aware of that let you know whether your tube doors are open. Hit Q once to open and hit it again to close. There is a message in the message window that says whether the door is opening or closing. You can always go to external view to see as well.
2- The Z key does toggle silent running on and off but it does not reset you to a prior speed setting when toggling off. You need to do that yourself.
Welcome aboard and happy hunting skipper.
