Yes, you can turn on HTML support, or auto-link, which will allow you to insert links. This may cause weirdness in the main calendar display, where event titles become links to event details, however. So you may need to change the template to not have the titles be links to event details.
Icons can be added as a custom field, yes. You could have a select box with names of icons, whose values hold the URL to the image. When displaying the event, output the value of the icon field into an <IMG> tag. That's probably the best or only way to do it.
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Scott
CalendarScript.com