Thanks for that info and choosing the Apple Support Communities. Based on what you stated, it seems you are experiencing issues with the Mail app on your new iPhone X. If you haven't already, please force close the Mail app and restart your device as iOS clears cached data and does other system optimizations when you turn your device off and on.
Next, use iTunes on your Mac or PC to backup and restore your iOS software to factory settings, as this process erases the information and settings on your device and installs a fresh copy of the latest iOS software. Temporarily setup your phone as new to test your issues, and then restore your backup and test the issues again.