I have a small L2S database that was generated with the L2S CreateDatabase command. When I add a class or property to the DBML, the database is not updated automatically. I get errors like "Table not found" at runtime.
Is there a way to add new tables and columns to a database?
No, LINQ to SQL cannot update your database schema to reflect changes made to DBML. To do so you'll have to either recreate your DB from scratch (which, granted, LINQ to SQL does not do very well), or use something like Wizardby to version and upgrade your DB schema.
No it is not. You need to refresh your Server Explorer, and then remove your changed table form DBML, then drag and drop it and CTRL + S :}
Not out of the box, but there are third party tools that add that kind of functionality. Take a look at my tools - Huagati DBML/EDMX Tools.
The add-in can generate the change scripts for you, and there is also a runtime component that can be used within your app to detect and generate SQL-DDL for diffs between the model and the database.