Hm. This is a very good question. I would say the answer depends on the context. The first sentence is missing a subject, and that is almost always an out-of-place construction in English. The only acceptable context I can think of in which this structure is acceptable would be on a resume or some kind of application in which one's qualities are described. In fact, not only is it acceptable, but it is actually preferred. In any other context I can think of, however, a subject needs to be added for it to be able to stand alone as a sentence.
The second two examples are both completely correct as far as syntax goes. The only thing you might want to consider is what you want to emphasize. It seems to me that the second variation emphasizes his qualities, but the third variation emphasizes critical situations.
There is only one correction that needs to happen. To make restrain into a noun, it should become restraint. So the first two clauses should say, "...self-restraint...". Also, while not a correction, if you wanted to use the correct form of the word "composure" in the third clause, it would be composed.
I hope this helps! Good luck!