At what stage of research career one can write a 'review article'?
First, I'll remark that (at least in fields close to me: physics and chemistry), the process for submitting review articles is typically handled in a different way than other articles (which I'll call “research articles”). Review articles take a lot of effort to write, and that their publication may depend not only on intrinsic quality and scientific criteria, but also on editorial policy: if the journal has already hosted a review on a given topic, it is unlikely to publish another soon afterwards. So, the common practice is to come to an agreement with the editor before writing the full article. Either the editor contacts a scientist to offer him to write a review on a given topic, either an author sends an abstract to the editor asking if the journal would welcome such a review (with no guarantee as to the results of the peer-review process, of course).

This has an important consequence for your question: you can actually ask the editor of the journal of your dreams if a review by you and your co-authors would be welcome. Practices may differ between fields, journals and editors, but asking exactly the person who is going to make the decision is the right course.

Then, we come to what I would call the “customs”. It is indeed typical to gain some authority in your field before writing review articles. This usually means working for a few years in a given field, publishing some articles of your own, in short: getting noticed by your community. As such, it is not a typical thing to do for a graduate student. Maybe at the end of your PhD, jointly with your adviser. Most probably, later in your career: either as an experienced post-doc, or after having gained a faculty position.

With more than a few years of experience, my personal experience is that you perfectly write reviews (and the editors will accept if the work is good). However, it gets easier with seniority, as you will (i) more easily have your work accepted in more prestigious journals, and especially (ii) more easily get invitations to write reviews.