MacOS multitasking: Reducing necessary key presses; "Windows" top menu bar

Parallels 19.1 / MacOS Ventura

Hello,

when Control Center is active and I select from Parallels menu (top left bar) the menu command that will hide Parallels (i.e., the control center!), this will subsequently conveniently cause my Windows VM's windows to show up irrespective of whether I select the Paralells Icon (red-white-blue) or the Windows VM's icon (typically a blue Windows symbol) when multitasking with CMD-TAB (or when clicking on the respective icons on the Mac Dock). This makes it possible to avoid having to press TAB twice when multitasking between Mac Apps and Windows VM.

If I do want to view the Control Center, I can simply right click on the (red-white-blue) Parallels Icon and select Control Center and it will show up again.

I'd like to ask three questions:

1. Is it correct there is no way to completely hide the Control Center from the CMD-TAB menu? (this is the question most imporant to me)

Not so important:

2. When I presse CONTROL-OPTION, that enables me to access the top menu bar (MacOS) to control a virtual machine, for example to remove attached devices or create a snapshot. I noticed that on the left of that bar, it says "Parallels Desktop". I remember seing the text "Windows" in that position, in the past. I seem to be unable to see that anymore. Is that a change in Parallels 19 or am I missing something?

3. When two VMs are running, and I hide the Control Center as described above, when clicking onto the Control Center Icon on the Dock to view a VM this seems to prefer showing one VM over the other (i.e., activating its windows/fullscreen). I cannot figure out the logic: I would expect clicking would show the VM last viewed, and subsequently toggle between the two.

Thanks for help.