Hi Tom,
You did not answer my previous message re the current organization of your moodle/mod folder...
From the error messages you quote it is obvious that you installed the questionnaire module in the wrong place to start with. Those messages tell you that moodle is now looking for moodle/mod/css/version.php; moodle/mod/css/images.php; moodle/mod//images/questiontypes.php files which of course do not exist there and should never have been there. You probably unzipped the questionnaire files to the wrong place in the first place.
What can you do now?
Logged in as admin, go to Modules/Manage Activities. If the Questionnaire module still shows up there, click on the Delete link.
Check the contents of your moodle/mod/ folder for any unwanted files there.
If this does not work, you may have to look into your Moodle database, using phpMyAdmin. In the mdl_modules table, if Questionnaire is still there, delete it.
Joseph