If I register a domain name, how can I use that for email? Do I need to have a hosting account now too or can I just somehow set up gmail to work with it?
You need to pay for hosting as well, since email is a hosted service. If you're going to go with Gmail for that domain, you also need to pay for hosting, as DNS is also a hosted service. Google doesn't provide DNS services.
Can't he edit his MX records without a hosting account?
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You don't get MX records unless you've set up a domain, which requires hosting.