How can I submit my form from my C# Silverlight code?
Simple: call one of the overloads of the static Submit methods exposed by the HtmlPage class:
HtmlPage.Submit();
HtmlPage.Submit( "formId" );
If you only have a form on you're page, then using the first option is the way to go. if you have several forms, you need to specify the id of the form you're submiting and you need the second overload. Simple, right?