That is not entirely true though, is it? The forwarded e-mails won't become non-Gmail over time and I will still be dependant on Google to forward the e-mails to me.
Somewhat. You have to remember to notice and tell everybody who sends to the gmail address to change. Some mail programs make this easy for your friends some do not. Over a few years people update their address book, and eventually almost nothing goes to gmail anymore.
Yes, forward them to your new email, preferably using your own domain name. Start giving out your new email to people, reply to your gmail email from your new email. It takes time but after a few years you can ditch the gmail completely.