I'm not sure if the drive for reproduction is purely psychological. There are also physiological aspects to it.
It is. Buddhas and arahants do not have it. So it is a question of a defiled mind. But, of course, mind acts in this world with the help of the body, it is strongly tied with the body, and so, defilements manifest through body.
With regard to the sutta that you have linked to. That is a teaching given to a specific group of monastic's at a specific occasion. I wouldn't take it to be the final word that "sexual desire is the strongest of all sensual desires".
Well, 95% of all suttas are given to monks. But that does not mean that this truth is applied to monks only..
Anyway, you can also consider this - different people have different interests and pursue different sensual pleasures. But sexual desire is common for all of them. This is the "base" desire. And certainly it is very powerful.
Well people get and want more than sexual intercourse from relationships generally. I wouldn't like to over speculate on this particular monk but it is also possible that the relationship was a means to an end or a symptom of a deeper disquiet. I think it is highly improbable that he left purely out of a desire to indulge in sex.
Yes, its hard to say, we dont know what is in the mind of this or that person. But I would not dismiss the desire for sex. More than that, as I see it, sexual desire is not just a narrow lust for some tactile pleasure. I see it as much wider idea of "being with a woman" (well, with the object of sexual desire).