Simple question, probably not a simple answer.
Can you create a new template and build several pages using that template?
For example: a page template that has a few specific sections, that doesn't replicate the same content over multiple pages, but allows customisation in each page independently.
You certainly can, you can create different product page templates. On the right-hand column of the product customization page, there is an option to change your page liquid, if you have more than 1 for a product page. It wont show unless you have multiple templates for the product page
You can not use product temple section to any other section, you have to create separate page template for that and then add section to page,
You can follow this video.
NO you can not use same template with different section on each page, for that you have to create new section for and new template for each pages.