Code first, although it allows you to send in some raw queries and hence perform your own native database/server manipulations, basically is designed only for building a model and querying upon that model.
Now as for your question: You can directly build 'stored procedure alternatives' by adding methods to your DbContext (or extension methods for seperation of concerns).
Triggers are a little more complex. You can override the SaveChanges method in which you can basically track each change made either before it got persisted back to the database- or after.
Both problems however can also be solved by introducing a repository. See: http://huyrua.wordpress.com/2011/04/13/entity-framework-4-poco-repository-and-specification-pattern-upgraded-to-ef-4-1 This allows you to launch a script (trigger) when adding, updating or removing a certain entity