How is it possible to manage windows with multiple screens and multiple spaces using just the keyboard?

(Tiling might solve this, but my main issue is productivity)

This involves a set of simple features:

  * Maximize windows
    (Move to another screen and it is still maximized
     even though the screen is bigger, crazy right?)
  * Cycle windows (on just the current screen and space)
  * Focus another screen
  * Move windows to another screen or space
  * Optional: Move the mouse to the focused window

I tried tools like Spectactle, Amethyst or Mjolnir, but it took only a few minutes to realize that something is broken or missing.

Is this somehow possible? How do you solve this?