In site.com studio, is there any way to dynamically generate site pages from a template without manually creating a filter (drilling down to a single record) in the data repeaters, for each page?
There is a way to create site pages from a template without the data repeater for each page. You can use Page Data Connections, which were introduced in Spring '14.
To add a Page Data Connection, you need to open the page or template and select the Page element in the navigation panel/tree to view the page properties. There is a section called Page Data Connection which allows you to edit the connection.
You can edit that to add the connection and specify something like a query string id parameter to filter to the individual record.
To then use the actual data, you can directly refer to any field using the expression syntax. For example, if you want to display the name field in the Title property, you can add it to the actual Title property of the page (as seen in first screen shot in this answer).
Additionally, you can access the fields directly in other data contexts. For example, if you add a Data Element to the page, all of the fields will be automatically available. .
For your situation, you can add the Page Data Connection at the template level and then use the data elements (or something else) on each individual page. Each individual page will show that it has the connection in its properties pane, but if you need to edit the connection or remove it, you'll have to do so on the page template where you added it.