In my seminar I have to present a paper which has many nice figures. I use LaTeX and would like to insert some of these figures into my presentation and handout. Ideally, I want these figures to be nice (not screenshots), so I am thinking of writing to authors and ask them to send me the figures they used in pdf format. Is it appropriate request?
The question is difficult to answer in the way it is phrased. I would find it hard to believe that there was a seminar activity asking you to find other people's figures and present them. There are lots of immediate copyright issues from doing that.
There is a certain amount you can do based around the fair use rules for academic use and giving acknowledgement to authors. The norm there would just be the screenshot, with the acknowledgement (the latter of which should cover the fact that image will not be of the highest quality).
But it may be that the request for high quality figures is really asking you to create your own, whether this means coming up with something novel, or generating your own (cited) version of the original figure.
In any case, I don't think that contacting the authors is appropriate here.