I already created a theme in WordPress and I can edit the page with the plugin “front-end-editor”. Now I want to know if I can split one page in different elements which can be edited separately? And if I can create a template for each element and built single pages out of combinations of these elements?
How can I edit elements separately on a single WordPress page?
Yes. Use the wordpress function get_template_part() it works like a standard php include() upon files without the .php extension in the same theme folder. For example to include a standard header for your pages add:
But, to be able to easily edit parts of a page in wp-admin (ie reusing parts of a page in several pages), the most native way I’d say is to use widgets for this purpose. A widget like “Query Posts” http://wordpress.org/extend/plugins/query-posts/ can be used for putting blog posts or even page content in the widget, hence you would achive what you are looking for.