Restful routing, restful versus non-restful routes

So resources :products will create 7 different restful routes for CRUD operations for resource products.
For example: products GET /products(.:format) products#index

So restful route includes only controller name within itself and :id for operation like edit, show, update, delete. When i create non-restful routes in rails for example: get ':controller/:action/:id' i only can see difference that i must explicitly write :action, so that ":action" makes this route non-restful?

** So
as i get this, first requirement for route(URL) to be restful is that route can’t contain action name?** Question 1

Second requirement for route to be restful is that action corresponding to route must “play by restful rules” in another word,
for
example a GET should not leave side-effects on the server, but just retrieve data.
So if i have /products(.:format) products#index and within index action i saved something into DB, than above route is just looks like restful route but in fact it isn’t? Question 2

I know that i can pass to restful route additional parameters, for example:
link_to “Show”, products_path(id: 5, a: “aaaa”, b: “bbbb”) so now URL is: products/5?a=aaaa&b=bbbb.
So am i violating restful here, or this route is still restful? Question 3

To me seems that i don’t need non-restful routes at all, when i can make a bunch of restful routes with construct like following?(and other similar construct) Question 4

resources :products do
  member do
    get 'preview'
  end
end

And just one more question, is there anything bad(maybe code smell or something) to make restful routes when i don't have model in database.
So for example, resources :sessions, where i don't have session model(no sessions table in DB). Question 5

Please don't redirect me to [http://guides.rubyonrails.org/routing.html](http://guides.rubyonrails.org/routing.html) i read it multiple times :)