1. If the app works while on your own network but not on 3G, check first to see whether it works when you are on wifi but NOT your own network. If it doesn't work while outside your network (wifi or 3G), then there is probably a routing problem. You need to have a static IP address or set up a ddns account (dlinkddns.com is free). You also need to forward the port used to access the camera. For example, if you choose port 8080 as your HTTP port under Setup/Network Setup, then port 8080 on your router must be forwarded to the camera's local IP address.
As for apps, I use IP Cam Viewer Pro. It is $4 (I believe), supports both the microphone and the speaker on the camera (although the sound is pretty choppy), and you can zoom in and out by pinching or spreading on the iPhone. Also, the developer is very helpful and responsive.
2. Joe Public is not quite accurate: version 1.0 of the firmware supports two events, not just one. It should support a video and simultaneous snapshot -- at least mine did. However, if you use the same media for two simultaneous events, it will not support both at the same time. Perhaps your video and snapshot are being treated as the same media. You might try setting the snapshot and video at different resolutions to get them treated as different media.
I do not believe there is a way to get continuous feeds using just the camera. Perhaps separate software could do it, but that would entail running a computer continuously.
3. I don't know of a solar or battery-powered IR illuminator, but there are plenty of battery powered security lights that go on when they sense motion. The light doesn't have to be infrared to provide enough illumination for the camera to operate.
