1) You can use the Page.ResolveClientUrl() property to properly parse
the ~ character.  The ~ essentially deails with virtual directories
correctly.

2) This can be done via the parsechildren attribute.

Lets say you have a WebControl Demo with a property Text.  To map the
Inner Html of the markup to the text property you would specify:

[ParseChildren(True, "Text")]
public class Demo
{
 public string Text
 {get; set; }
}