Firstly, is there a way to get Armory to display the current number of active connections (like bitcoin-qt does) when it's in online mode?
In Armory, go to File -> Settings and uncheck the first box. This setting allows Armory to control your local instance of Bitcoin Core. By turning it off, Armory expects you to manage Core manually. At this point, you will have to start BitcoinQt yourself, then Armory. On the other hand, you'll get to manage your instance of Core the way like, and get stats directly from its GUI.
Secondly, how do I get Armory to display balances in uBTC instead of BTC?
Sorry, we never got to implement that. We had a design discussion about it but didn't proceed further due to other priorities.