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Boris, this will come as no surprise to you, but I believe in Angels (though I won't agape--second definition in your dictionary reference, not the first regarding 'love'-- the crowd with the 'whys' or hows). From whence come these beings? They exist (as far as I'm concerned) in a realm, a reality; what is the nature of that reality, as it differs from our reality our perception? I have a sneaking suspicion their realm differs mostly in temporal orientation rather than spatial orientation alone.

Time, as well as our three dimensions of space, is a created dimension. Einstein helped us to understand that time is not something apart from space, but is intimately connected with it, as is matter and energy. Thus the Creator exists "outside of" and independently of our space-time continuum, but we do not exist outside or or independently of our Creator. You could do this concept as a Venn Diagram: you would have a rectangle with diagonal lines, and then a circle within having both the diagonal lines and a different set of diagonal lines.

This suggests that there is some sort of extra-dimensional realm of being outside our own three dimensions. Angels must be inhabitants of that realm, but they must be able to imperceptably interact with our realm, just like a sphere can intersect with a plane at a single, infinitely tiny point.