Considering this purchase for my P3P.  I was wondering if I will still have full display on my Apple Mini 4 as normal AND can view everything simultaneously through an external HDMI computer monitor?

Yes, you will have everything still on the Mini (as long as you have Simultaneous image output to app and HDMI enabled) it's in the image transmission setting page.
And you get basic telemetry on the monitor (not everything on the Mini) if you have Display OSD on HDMI Output enabled.