I am not quite sure which version of the Telerik.Web.UI assembly you use, but in case you are using the latest version (Q2 2010 SP1), the slider should be visible in all supported browsers but Safari and Chrome.
Basically, the problem is a result of the fact that fancybox uses "display:none" style setting to hide the box. As a result, the slider is initialized in an invisible parent and it cannot calculate the size of its elements correctly. In order to fix this, you should call the repaint/redraw method of the slider
as soon as the fancybox shows.
Regarding your second question - you can either ajaxify the slider control or use its client-side events
to call a WebService method that updates your database.
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