First question, adding fields above the Name and Username. That page is rendered by the core component com_user which is part of Joomla! itself. Customizing Joomla! is outside the scope of our support. Just for your info, what you are trying to do is not possible. Plugins can only add fields below the core fields (name, username, password, email).
Regarding your second question, how to remove the Akeeba Ticket System signature field from com_user pages: unpublish the User - Akeeba Ticket System plugin. Please note that this makes it impossible for users to add or edit their ATS signatures. You cannot selectively remove this field e.g. when subscribing. Joomla! has a single event firing any time it displays a user editing form, frontend or backend, registration or profile edit. As a result we can't make the field disappear selectively. At best you can change the Access of the plugin to a view access level which only includes the user groups which have access to the ticket system. This way you are effectively showing this field ONLY to people with access to the ticket system and ONLY when they are editing their profile.
Nicholas K. Dionysopoulos
Lead Developer and Director