Hello Ed,
At this time there is only manual registry edits to make it possible to register OC as default folder handler. You can find it in this forum but I can only recommend it if you had to restore registry before; I have missed some \ or other character before and made bad registry entries, and restoring it is not fun. It is tricky in this case because if you do that the File Explorer becomes useless and even clicking a folder in File Explorer will try to open OC. I have not tested it much as I have to run OC from development environment all the time, so I'd need to test it more before I know how well it works. After the official release I will make a button in settings to register it in a safe way, so it may be better to wait.
OC runs in background for faster start and to keep the any ongoing copy/move operations alive, and several other reasons. To close it you can right-click on icon in System Tray and click close, or hold Ctrl while clicking the window close button.
Running as admin won't show shares because admin is a different user, so program runs in that user's context; Windows works that way. You'd have to mount those drives from OC so that user also to be able to access these... but I have just realized that Drives>...>Map network drive won't work for that if the network drive is password protected, so I will have to add that soon. I have just tested and accessing network shares directly by typing the path \\comp\share does work and uses already saved Windows credentials (I didn't expect it to work, but Windows is weird). If you can access those that way, you can also add these to favorites for easier access next time