Several questions concerning CI4 controller

What I'd like to know is how CI establishes the connection to the (local) postfix server and how it uses its resources to write out into the web, read mails etc. pp.

CI gathers the config setting and other inputs (e.g. to, from, subject, etc.) and passes them as arguments to the mail server executable (e.g. Postfix, Sendmail, Exim, etc.) installed on the computer hosting the webserver.  After that, it is all up to the mail server program. When the mail server exits it returns a status to CI that ultimately shows up as the true or false that $email->send() returns.