Buy a domain, buy a offshore vps or offshore hosting or use a spare pc in your home and become the email provider yourself.
This is not a good idea, there is no way in hell you can get this secure enough, even if you know what you're doing.
2nd problem is, most mail provider you send mails to will treat your mail as spam.
2nd problem is not true, it depends on your hosting ip. If your hosting ip is flagged as source of spam your email will be flagged, but if you are using clean hosting ip your ip won't be mark as spam.