During the course of your daily sessions of prayer, you say, the Name of Allāh has occasionally “interposed” itself while you were repeating the Jesus Prayer, and you want to know what I think.
It goes without saying, of course, that there’s nothing “un-Christian” about invoking this Name. As you doubtless know, Allāh simply means “God”, and this is how Melkites and other Arabic-speaking Christians would normally address the Deity. On the other hand, as a matter of spiritual method, it’s obviously inadvisable to mix divine Names when engaging in Prayer of the Heart, the aim—or at least one aim—of which is a deepened concentration leading to hesychia or imperturbable stillness. There is also this methodical point to be noted: to say—as you did in your letter—that this interposition “just happens for no apparent reason” suggests a lapse of attention on your part; otherwise you wouldn’t find yourself doing something you hadn’t intended.
Do I think you’re “in danger”? No, but I do strongly advise you against giving place to this Name during your formal sessions of prayer. You speak of having sometimes deliberately stopped the Jesus Prayer in order to invoke Allāh “several times” before returning to the Name of Christ. This is unwise. My counsel, on the contrary, is that as soon as you’ve noticed this phenomenon, you should immediately turn your attention back to the words of the Jesus Prayer, gently but also firmly and insistently. Of course, as I’ve already noted, there’s clearly nothing wrong with a Christian calling upon the Name of God as such—or rather the Name “God” as such, be it Deus, Theos, or Allāh—rather than an avataric Name. If you feel a strong desire to invoke Allāh, you should certainly feel free to do so outside the formal invocatory sessions.
As for attending the Buddhist “gathering” you mention, it’s certainly possible—indeed highly desirable—to learn from the other traditions, but I would very strongly caution you not to join in any of the actual practices this retreat may entail; anything that might in any way compete for “psychic space” with your rule of prayer should be assiduously avoided. Listening to the lectures is fine, and so is “just sitting” or breathing, or even endeavoring to watch the inward movements of your mind. But if you’re invited to engage in a visualization of a Buddhist mandala or dakini, or to invoke a Buddhist mantram, you should obviously not do so. This should go without saying, but sometimes restating the self-evident is important.
A final word of warning. Each of the questions you’ve posed suggests you’re bored, or discontented in some way, with the very simplicity of the Christic invocation. It’s true, of course, that there’s something “monotonous” about the Hesychast path, but holy monotony is precisely one of its strengths! For its part the ego wants some novelty to escape to or some complexity to hide in, whether it’s making use of an alternative mantram or investigating the teachings of another religion. The efficacy of our method consists in the fact that we systematically avoid fulfilling this egoic desire, turning our attention repeatedly back to the “one thing needful”. Nothing else matters; in fact nothing else even exists.