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How common is the practice of praying for the devil ?
It is usually encountered within Eastern Christian monastic literature, as an aspect of engodment. (I am in my late thirties, and have read dozens of Romanian books on Orthodox spirituality, starting with my mid-teens: I'm afraid this is as best of a source as I can offer, given various linguistic barriers). Personally, I've never encountered it anywhere else, either within the faith itself, or within other denominations, to the extent to which I am more or less aware of their tenets and traditions.
The main meaning or motivation behind it is one of unconditional love for and forgiveness of all creation, (mortal) enemies included; that does not mean that the latter will automatically embrace it, or even offer a positive response, merely that those engaged in it have become one with divine goodness, by embodying God's infinite loving-kindness; perhaps a good introduction to the concept would be Alexandre Kalomiros' River of Fire, with the disclaimer that its Greek author seems quite fond of engaging in more than a fair share of (potentially inflaming) anti-Western polemic.
The two Church Fathers who are most famous (at least in the modern era) for having been universalists, namely Origen, and Gregory of Nyssa, are incidentally also the ones known for having espoused the idea that not only all humanity was or would be saved by/through Christ, but that the devil and evil spirits/entities/demons in general, as logikoi, i.e. rational beings, are likewise beneficiaries of this aspect of God's grace.
As far as I have read, neither Origen nor Gregory mention such an idea.
Not only do they not mention it, but the former is quoted by another ancient writer, possibly Eusebius, as explicitly criticizing it. (As I already wrote, the underlying mental state behind these prayers has little or nothing to do with Origenism, which has already been formally condemned by the fifth ecumenical council).