Strictly, the answer to all your questions is: no.
Depending on device, you may be able (manually) to configure a WLAN access point as the default for that application.
On Series 60 3rd Edition FP2 and later, you can find the currently active connection type by:
This should return "wlan" if a WiFi connection is active for that application. Check the Nokia Java Developer's Library for other values (downloadable from the Documentation section of this forum).
String connectionType = System.getProperty("com.nokia.network.access");
The only way to see if the connection actually works is to try it, and see if it fails. I don't think you can check WiFi signal level.
Hope that helps. Probably not much.