Why is there a  tag where I didn't add it?
For not getting the paragraph tags, you need to use an input format that does not include the Lines and paragraphs break automatically setting.

Check to see if Convert line breaks into HTML input format is enabled in admin/config/content/formats/full_html, and disable it. You can still add &lt;p&gt; and &lt;br&gt;, but Drupal will not add them automatically for every line break present in the text.