How should I address other people in languages with a tu/vous distinction?
Unfortunately, there is no general rule covering every situation (or every language).

However, a good rule of thumb is to just use the "vous" when you are not sure which one to use and then imitate the other person.

If you are more senior you probably can also offer using "tu", especially at the university, but with the rule from above you can be sure that you are not being considered rude.

The generally accepted way to address professors unfortunately differs from university to university (in my experience more than from country to country), so I suggest you use the rule from above.

With fellow graduate students and postdocs, you are right, you can in general use "tu".


  Does the answer change depending on if you see the person face-to-face
  or if you write them a letter/email?


No.

(This might be specific to Germany and France, but I guess at least in Spain this behavior would also be fine.)

Addition: If you are on a first-name basis that usually means that you are allowed to use "tu" (at least in Germany this is generally accepted and from my observations this is also true in France).