How can I get rid of these error icons and query highlighting?
Steps below:
Right click the error marker and select "Preferences"

Expand "SQL Editor" and go to "Code Editor", deselect "Show problem markers" under the "Miscellaneous" category

I prefer to show the error highlighting as a debugging aid. Often though, it sticks around long after it's no longer useful. To clear the highlighting in this case you can right-click on "Errors" in the problems dialog and select Delete.