First, make sure that your OS and iMovie are updated to current. If you are using Mojave you might want to keep it there, as Catalina sometimes has some quirks, particularly with the Photos app that it automatically updates.
Try booting up in Safe Mode (see Finder menu for instructions) and then, after everything loads, immediately shut down and reboot in normal mode. Then do your delete preferences again by holding down the Option and Command keys and selecting to delete preferences in the box that appears. iMovie should open in a new library. Reopen your old library to get back to your projects. Now see if you can share out at 1080p and if the pixelation issue is cured.
Also, you won't get the 1080 share option if the resolution of your project is set more than one stage lower. iMovie sets the frame rate and resolution of a clip at that of the first video clip (not photo) placed into a newly created project. So create a new project and insert your 1080 clip as the first clip. You can check the resolution of the project by clicking on the Settings Button above the timeline at the right hand side of your screen. Look in the little box at the top of the dialogue box that appears when you click on the Settings Button. It should say 1080p if the first clip placed in the project is 1080p. Then try to share out and see if you get the 1080 option.
If you are still not getting the 1080 share option, you might try redownloading iMovie.
As for the pixelation issue, that has been mentioned several times on this forum, but usually with the Catalina upgrade. If the things mentioned above haven't solved it, you might try changing your iPhone "Transfer to Mac or PC" settings to "Automatic" to get the most compatible export format. Sometimes the HEVC format can cause some issues.
-- Rich
