Add this to your config.js file:
config.autoParagraph = false;
config.enterMode = CKEDITOR.ENTER_BR;
config.allowedContent = true;
That should fix the p tag issue.
The line break issue is a bit more complicated. Of course you can edit the .css so that the LI element doesn't display those line breaks, which is the default anyway, you must have custom css to make it show.
The other option appears to be to add a plugin to your editor. I found this in a google search on the subject: