First, you have to understand that the Home Page originates from the concept of a document hierarchy. Where the top most document is referred to as the home, and all child documents in sub-categories are its descendants. To navigate from any given point in the hierarchy to the top was to return Home.

A Home Page is only possible when a document structure exists in the current context. There are many possible website designs that don't follow a hierarchy, and therefore a home link isn't effective. Pinterest has a never ending image feed as you scroll down, and other websites have everything on a single page.

In a document hierarchy the most common place to locate the table of contents is at the top on the first page. From there you can navigate deeper into the hierarchy. If you don't keep meaningful links on your home page, then why send visitors there? There is no rule that says the home page has to be the table of contents, and more websites are relocating these links to sub-sections like /news or /blog where people can discover deeper content.

A home page and a landing page are the same thing. They both represent the top-level of a document hierarchy. Many websites create micro-sites that have their own home page, and use that home page as a landing page for marketing campaigns. When a visitor arrives at the micro-site they can read/discover information regarding the promotion they landed on.

When a visitor is in a micro-site the Home link may take them back to the landing page rather then the main domains root. This is perfectly acceptable, because the landing page can be thought of as the table of contents for the micro-site. As long as the visitor is able to quickly find what they need. There is no problem.

What's better? Disallowing users to go back to the sales/landing pages, and redirecting them to their content/dashboard home?

Relative context is important to users. There is no benefit in directing them to the sales page if they have already purchased. You should not block those pages, but simply take them to their dashboard. If someone says but then they can't… then the problem is with the dashboard, not where you redirected them.

or redirecting them back to the original home page when they click home?

For logged in users. Move the Home link to the footer, and replace the upper menu Home options with the word My Dashboard or My Home, and then take them to their dashboard.

Should the root page even be called a home page?

Technically, http://www.example.com/ is the home for that entire domain, and http://www.example.com/blog/ is the home for the blog, and http://www.example.com/blog/features/ is the home for the features category. Home is relative.

What should it be called?

I don't know when the word Home started to be used, but it's actually the table of contents and that doesn't sound very good. So call it anything that explains this page gives you info about other pages. Words like Home, Portfolio, Gallery, Folders, Contents, Categories, etc. can all be thought of as home pages. It's all relative to what they index.