It's possible update a polymer element without reload page? If I do this with ajax, I have the error "a type with that name is already registered". What I can do?
Flavio is right here. You need to change your PHP code.
For example, change the PHP code to return, say, JSON of the result of sending a GET request, which would be the result of the SQL query.
Then, in Polymer, create a component that calls that via Ajax. The component could update the aforementioned query from input values without need for a page refresh, including initially getting values from URL parameters.