first I want to be able to click on link in my website and make it
appear
one of those smalls screens for the user to type the message, email,
etc,
and send this email to the admin.
second I want to make something like those supports that you type the
email
and text in the browser, press send and it sends an email to the admin.
Your e-mail server refuses your connection. Either it doesn’t allow
SMTP relaying at all, it uses POP-before-SMTP (what most e-mail
clients do: fetch new mail, then send off queued mails) or you have to
authenticate.
In any case, check your hosting provider’s requirements, check the RoR
docs on e-mailing and fix it.