Hi: great questions!
All sorts of customizations are possible. Check out our Themer’s Guide in the first instance as it gives a great overview of the basics involved in making custom changes – then our tutorial on adding thumbnails to the events list widget would be the next thing to look into.
The event list widgets I see on your homepage seem to have been customized quite a bit, though, so it might be you need to adapt it accordingly. Similarly, without knowing what changes have been made there trying to guide you through a date format change could be tricky.
See how you get on with the Themer’s Guide and tutorial, though, and we can take things from there 🙂