Entering data into SharePoint lists via Silverlight forms

There shouldnt be any problem using CSOM (.NET client API reference for SharePoint 2013)

Example code:

// Starting with ClientContext, the constructor requires a URL to the 
// server running SharePoint. 
ClientContext context = new ClientContext("http://SiteUrl"); 

// Assume that the web has a list named "Announcements". 
List announcementsList = context.Web.Lists.GetByTitle("Announcements"); 

// We are just creating a regular list item, so we don't need to 
// set any properties. If we wanted to create a new folder, for 
// example, we would have to set properties such as 
// UnderlyingObjectType to FileSystemObjectType.Folder. 
ListItemCreationInformation itemCreateInfo = new ListItemCreationInformation(); 
ListItem newItem = announcementsList.Items.Add(itemCreateInfo); 
newItem["Title"] = "My New Item!"; 
newItem["Body"] = "Hello World!"; 
newItem.Update(); 

context.ExecuteQuery();  

More info could be found here: http://msdn.microsoft.com/en-us/library/fp179912.aspx