1) Check the logs of HAM (hildon application manager) which should be available. If you could not make sense of what it is saying use FAM (faster application manager, also known as fapman) and see if you can get a more useful output.
2) Usually if there's issues with HAM you would see banners appearing on the screen such as "Operation failed". This may also happen when you have enabled large amounts of repositories or repositories that were meant only to be for testing such as extras-{testing,devel}
To reflash your device read here.
3) Widgets and stuff disappearing could be because you have either installed programs which were specifically marked for testing or unstable and they have caused issues. It could also mean that your hildon-{home,desktop} is crashing due to some issues with your device.

If your hildon-{home,desktop} crashes, you can easily see the task tray icons that you used to see at first and subsequent bootup is either lost or had to be refreshed and your widgets on the home screens vanished. I would suggest you install something like CPU/mem applet which will show you a nice little usage status in your task tray. Usually when a crash happens you will see the first bar (left one) jump up to 4 bars and starts indicating red block on the uppermost block.