Like you stated it won't tell why it has lost connection. It could be running but maybe the router is down or It could be a wireless bridge connection issue if you use one (I always highly recommend hardwiring your apex even the new model, it's simply more stable).
I like that idea.. Can you share how you mounted your camera? How far do you keep it away from the tank? What is the impact to your wifi? I actually would love to check on my fishies during the work day.. so I could just log in and see my tank all day every day?
I don't know what your budget is, I have a Yi web cam on my home. It's enough to see what's going on and if it's off chances are the power is off. They also make Wi-Fi power alert plugs i believe. Under a hundred bucks but it sounds like you're interested In something a little more Intuitive??
Covered above but....Unless you have the apex brain connected to a ups it technally doesn't alert you to an outage. It does tell you when it has lost fusion connection, which most often is power outage related. The next most common could be loss of internet.