Any styles in the document will be used in preference to others if they have the same name.
Any styles changed in the template after the document was created will be available as changed to the document by updating styles. Absent such updating they will not be available.
All styles in Normal.dotm / Normal.dot are available to all documents. Those styles already in the document will not take on the attributes of styles in Normal.dot unless you update them. (Normal.dot has many more styles than are ever used in one document.)