As for emails, dude you can create a ton of emails, not really something they can trace to you if you actually tried to.
I strongly disagree. While disposable emails are certainly a way to get rid of having your real personal info sold everywhere around, a 3-letter agency would easily find out which emails are yours and which aren't. Emails are not anonymous at all, and I am more than sure that NSA or CIA do have access to most, if not all email server backends.
It really depends. To a certain extent, you can make it really hard for them to track the burner emails back to you. A combination of Tails, Tor, a privacy respecting email service(or a burner email service like guerillamail) and doing your shenanigans on a public wifi could put you in a good position in the anonymity spectrum.