To get rid of the P tags, you can look in the "Custom" folder which you will find in the "HTMLEditor" folder and then look for files like content_insert_ContentValue1.js... you'll also see the one for update. You need to edit both of them around line 34... you will see:
FCKConfig.EnterMode = 'p';
Change this to:
FCKConfig.EnterMode = 'br';
This will insert break tags instead of the paragraph tag when enter is pressed.
However, if you want to completely remove the chance that your client can do any formatting, you could just get rid of the HTMLEditor instances and replace them with text areas which is your best bet.