Is the salutation and/or the signature of an email indicative of the intended level of formality? I wrote an email recently to the author of a book. I'm working on the master's degree in Hungary, the author is a professor in Canada. I'm not a native English speaker. My letter looked like the following:

Dear Dr. [professor's full name],
[body of the email including an introduction with my full name]
With best regards:
[my first name]

When I write to someone for the first time, I make the salutation and the self-introduction formal. But I tend to write my first name as the signature because I feel this shows that I don't insist on keeping the high level of formality I started the email with. In subsequent emails I choose the level of formality to be the same as it happens to be in the reply to my first email.
However, the reply to my quoted email seems to me to be so informal that I don't dare to imitate its level of formality without asking for the international academic community's, i.e. your suggestions. Their letter looked like the following:

Hi [my first name],
[body of the email]
Best, [professor's first name in diminutive (!) form]

So is a signature usually indicative of the intended level of formality? Would it be appropriate to start my reply like this: &quot;Dear [professor's first name],&quot; or &quot;Dear [professor's first name in diminutive form],&quot;? Or can my habit of &quot;imitation&quot; backfire often and make me seem insulting?
In my experience, the salutation often indicates something about the level of formality, while the signature typically conveys much less.
The signature is effectively meaningless because many people automate the signature on their emails, so it is literally not something that they are thinking about. Sometimes it will indeed convey a person's preferred level of formality, but since it's so often automated, that's not a safe assumption to make.
The salutation, on the other hand, is something that people definitely use to indicate their assumptions about the nature of a relationship. You don't really have a choice here, because pretty much every culture uses choice of salutation to indicate assumptions about level of formality, and even omitting the salutation has a meaning. Most readers will at least notice level of formality, even if the more cosmopolitan are unlikely to take offense.  Similar things apply in other choices as well for languages where relationship is strongly reflected in pronouns (e.g., usted vs. tu in Spanish) or other linguistic options.
If you are in doubt, it's usually better to assume a higher level of formality. People are generally appreciative of attempts to be polite, whether or not they are needed.
Thus, for example, in the particular case that you cite, Canada is a fairly informal culture, and the professor has almost certainly indicated that they  are comfortable with you using more informal language. If you are not comfortable with that and continue to say &quot;Dr.&quot;, however, they will likely just take it to mean that you are from a more formal culture and trying to be polite.