Compare page without compare button

Yes. Create a new menu item of the type "comparison page" and in the options of the menu, select the products you want for the comparison page.
Then, when you click on the menu item, you'll get directly to the comparison page of these products.

You need to turn off the "Activate compare mode" option of the configuration.

That's not normal.

Change the line:
if(empty($this->elements) || !$this->params->get('show_compare')){
to:
if(empty($this->elements)){

in the file "compare" of the view "product" via the menu display>views and that should fix that.