I use wipr. Also works on Mac - no problems and no ads

I didn’t bother customizing the dock. I always use the search and launch method to use apps. I have all home screens disabled anyway except one main page.

ApplePay and approving logins from 2fa apps - plus approving app installs/removals on Mac are the main things I use every day. It’s nice enough to have that I notice when I’m missing those things.

iPhone mini would be the regular size.

Well, you won’t be able to listen to music with Applecare+, but you will with airpods.

Which do you need?

How do you know the iphone is actually switching vs just rendering things to what it needs?

The screen blacks out on HDMI changes like those because there is a re-negotiation of the link between devices.