Hi,
Contact form: if you enable Google reCAPTCHA (AdminCP -> Core -> Registration), it will be used on the contact form. Whilst this doesn't stopĀ
allĀ bots, it should help with the issue.
Favicon: in Nameless v2, you can upload the favicon to the Nameless root directory (/var/www/html in your case).
Buttons in top menu: this is all done through the template files (in the case of the Nameless website, index.tpl). I can't help too much with customisations as it's down to what you want, but the Bootstrap docs can be found
here. You can also view the page source of the Nameless website (right click -> View Page Source) to see the HTML for the buttons.
Authme password resetting: this isn't possible yet I'm afraid, but it's a good idea and I can certainly look into it for a future update.