Is it normal to reject a paper based on the review of a single referee?

It is normal. Often there is one referee who writes an extensive review, whose judgment weight heaviest with the editor. If there are 4 reviews, 3 are in the "publish" half of the spectrum but are brief (not adequately justifying the recommendation), and there is 1 "reject" review which extensively argues against publication, an editor will either have to apply his/her own knowledge of the field and decide which argument carries the day, or will need to request an additional review. Good editors do not just count up the plus and minus values, they have to evaluate the evidence in the reviews.

If you make the case for reconsideration, I think it should focus on the question of whether positive evidence in the reviews has been undervalued. There's not much you can do if the negative reviewer is (unbeknownst to you) The Leading Authority.

In my experience, it is typical for papers to receive either zero reviews (editorial rejection) or multiple reviews (usually 3-4, but occasionally 2 or 5). Having just a single review (accept or reject) is very unusual. One possible explanation is that the editor formatted their editorial rejection as a review; another possible explanation is that you were dealing with a publication venue with a rather slipshod process.

You can email and ask for clarification. It is not, however, likely that you can get the decision changed in any way: if the editor found your paper problematic enough that they willing to reject with a single review, they are unlikely to change their mind on for purposes of "due process." Improve the paper, find a better venue, and move on.

It happens -- at least it's happened to me -- and although I don't know about the etiquette of asking for reconsideration, if you believe the bad review is based on an incorrect reading of the manuscript, then I think it's warranted.

The time this happened to me, I had two very good reviews on a paper and one really bad review. The two good reviews were short because they liked everything in the paper and had nothing else to say. The one bad review was bad because the reviewer was biased against my premise and did not examine the evidence I presented. I contacted the editor and pointed these things out and eventually the paper got published. So, there's not much to lose by touching base with the editor unless in your situation doing so would be a serious faux pas.