This is possible with Better Touch Tool. See: POWER USER TIPS FOR MANAGING SPACES (MACSPARKY LABS). This requires that the window be selected.
I do not know a way to accomplish 2 or 3 from your list. I’ve not come across a window management tool that can work across spaces/desktops. It would sure be nice if Apple provided a mechanism to allow this.
What I do is for my use cases, which are to initialize a working context, is to first move to a space/desktop and then open the windows. This is done with Bunch. Then I have Moom arrange the windows. This post provides an example: March 2022 Software of the Month Club: Bunch - #2 by MevetS
Hope this Helps.