Welcome to iPhone Forums!
It’s possible that you can change some of this in your settings.
In Settings - Display & Brightness, go to Display Zoom -View. If “Zoomed” has been selected, choose “Standard”. This should help with rotating to landscape view.
The screen will dim when Face ID detects you’re not looking at the display for some time - the timeframe is set by Apple. If you prefer your device to lock after the seconds/minutes selected in Display & Brightness - Auto-Lock, go to Face ID & Passcode, and turn off Attention-Aware Features.
Face ID has worked better for me than Touch ID, since the very first day I’ve started using it. That’s also the experience of most of our members. Tbh, you’re the first person complaining about it. Maybe resetting it and setting it up again will help?