I think implementing the entire website through one CMS that is on an e-commerce that has security in mind would be most desirable, rather than using a general open source widely used CMS and then using an online store plug-in.
Yes I believe that is true.
You can create as many pages you want outside of ShopSite and link them to the store using <a href...> links. Examples of such pages would be a main page, a contact us page, an About us page etc. So that is not a problem.
I don't understand where you are going to put the products that the client is trying to sell. If you don't want to use Order Anywhere links or use ShopSite templates or create a custom template for the pages the products are on, how will they be displayed so people can purchase them?