Yes, this module includes a separate CSS file, especially for the look and feel of this module. Take a look in the settings section, under Stylesheets you can find a file called umbracoFAQ.css.

There you can edit all looks for the categories, questions, and the form to submit a question.

Yes that is possible, there is a form to give your users the opportunity to submit questions.

You cannot use the form on pages other than the FAQ or a specific Category in the FAQ, this is made so to prevent Question nodes to be appended to unsupported places in your site.

You can disable the form for each category in the properties of a category on in the content section.

Well, there are 2 places you need to be,

1. to change the functionality of the lists (category listing or question listing)
   you can do that in the developer section in the umbraco backend, under XSLT Files you will find 2 files called Faq List Categories & Faq List Questions.
2. to change the functionality of the form (submit a question form)
   you will need to dig a little bit deeper, this form is a custom build user control which you will find the control (AddFaqQuestion.ascx) in the usercontrols directory of your umbraco installation.
   And the codebehind (AddFaqQuestion.ascx.cs) and designer file (AddFaqQuestion.ascx.designer.cs) in the app_code/Umbraco.NitroFAQ directory of your umbraco installation.

Yes, the umbracoNaviHide property is added in the properties so you can choose to hide certain questions or categories from an automatically generated menu or site map.

Yes it most certainly can.
It supports categories and just a single list of questions.

In the content section you can add a new category under the FAQ node.

However, you do not need to add categories. If you want just a simple FAQ on your website with only a few questions you can add them directly under the FAQ page.