So who are you hiding from? If it's the government, then you must use strong cryptography no matter where you host your email, and you must ensure that everyone you communicate with is as paranoid as you. (I would encrypt all my email, but nobody else I talk too will. So it doesn't work.) If it's advertisers you want to avoid, just run your own server and stop worrying so much. People have been doing it for years.
(Although, I run my own mailserver and am inundated with spam. Thousands of messages a day. So you aren't really avoiding advertisements, you are just avoiding advertisements for stuff you might actually want :)
That is illegal and ineffective. Full-disk encryption provides much more safety, both legally and technically. (They could still sneak into your house and install a hardware keylogger that gets your encryption passphrase, and then seize the disks. But this is real life, not a movie.)
Note: IANAL
You? Not so much. If the FBI shows up at your door, you're toast.
(Hint: the opposite. The government had to pay him damages for seizing his computers.)
One could make the case that hosting on Gmail has greater privacy in this respect, since if you send to any other Gmail address, the e-mail probably stays within the Google network.