In general things look ok but I can see where there might be some problems. It looks like your trigger is set to if (isset($_POST[""])) and your submit button does not have a name or id.
You should first update the submit button to have a name and id, then you should update the trigger for the server behavior to be based on the submit button pressed. This should allow the server behavior to be properly triggered and insert the records.
Let us know if you continue to have any problems with this and post back with a sql file for the table structure you are trying to insert into. I can do some testing with this to help determine what the problem may be.