What version of Premiere Elements are you using and on what computer operating system is it running?
I read of your "no matter what", but please allow me to focus on details since the believe that the answers are in the details.
1. What is the brand/model/settings for the camera that is recording your video? If multiple cameras, then pick one which ends up with the
worst results after import/editing/export in Premiere Elements. I am trying to determine the properties of that source media, including file
extension and whether interlaced or progressive video
2. What are you (manually) or the project (automatically) setting as the project preset which should end up matching the properties of the source file?
If you have a Timeline with multiple formats, just stick to one for this troubleshooting. See Edit Menu/Project Settings/General.
3. When the video gets to the Timeline is there no colored line or a red or orange line over that Timeline content? If a red or orange line over the content, does pressing the Enter key of the computer main keyboard help once the line is a green color? When you leave the Edit area after your edits, what is the quality of the Timeline content playback in the Edit area monitor?
4. What is your intended export - export to a file saved to the computer hard drive or burn to disc?
If export to a file saved to the computer hard drive, what is your choice Share or Publish+Share/Computer/then what? What Preset? And, are you using
the preset's default settings or customizing them under the Advanced Button/Video Tab of the preset?
Lots of questions. If there are any that you do not understand, please let me know, and I will re-write if necessary to communicate what I need to know to be able to help you.