Is it common to claim co-authorship by helping writing a paper without doing any research

people who help write papers may help fulfill one of the pillars of scientific discovery... communication of the science.

There is an appropriate place to credit people who read your paper and offer useful comments on it: the acknowledgement section. It is very common to see acknowledgements "for providing valuable feedback", "for suggesting a cleaner presentation", "for pointing out important related work" and so on. Even "for providing a simpler proof of Lemma X.y".

None of this rises to the level of co-authorship.

What's worse in this case is that

At the end, he will claim the co-authorship of the paper.

While I'd find the idea of co-authorship for such contributions odd, I would not think too much about it if it were negotiated in advance (as is the theme of many of the answers on this site). But to offer what appears to be unconditional help first and then (when the student really has no choice in the matter) to demand co-authorship is plain wrong.

To answer your last question on what to do, the answer, as is always the answer, is to negotiate things up front. It's a little awkward, but a little pre-collaboration awkwardness is MUCH better than a lot of post-collaboration recrimination and hostility.

The so called Vancouver protocol (developed by ICMJE (International Committee of Medical Journal Editors) and its definition of authorship has been mentioned in many questions of this kind here on Academia but I think they deserve being repeated. The protocol describes authorship through three components which every author must fulfil:

1. Conception and design, or analysis and interpretation of data

   AND

2. Drafting the article or revising it critically for important intellectual content

   AND

3. Final approval of the version to be published.

A key point here is the "AND". To read and comment on the text is clearly not enough for authorship by these standards. In fact a reviewer of the manuscript would at least fulfil point 2 whereas a person helping out as you describe would not.

It is difficult to fend off this behaviour from more senior colleagues as a PhD student. It may, however, be good to bring up an open discussion about authorship standards in the group without necessarily directly connecting it to the draft of a paper. In some research groups systems for determining both order and authorship as such have been developed by splitting the paper up into tasks. See for example, AuthorOrder.com for an example. Looking at the authorship tag here on Ac.sx and a search on Google will provide much background. But, I particularly recommend the recommendations report from ICMJE; ICMJE developed the protocol and their recommendations constitutes their continually updated version of the protocol.

Obviously his service and helps do not count as co-authorship. I have seen various versions of this tactic before, for example in the form of showing interest, or giving some general and mostly useless advices, comments and discussions. None of these are co-authorship either.

But to answer you question on "how should I react if someone wants to do the same to me?", I recommend you restrict your research communications to a small list of people who have the following qualities: 1. they are experts in the subject your are working on, 2. you have some kind of agreement about how to perform the research and who should do what, 3. they have scientific integrity and are not looking to get credit for something they have not done!

Finally, it is not recommended that you show or discuss your work to someone who is not a trusted expert before submission.