Thus, Angels are in fact multi-dimensional creatures. They can come and go into our dimension, assume any shape they like in our dimension
So far, so good.
and can occupy the same space at the same time in our dimension.
That's not clear at all.
First, God (I'll capitalize it as a proper noun) is described (not in the bible) as omnipitent (all powerful), omnipresent (everywhere, presumably at the same time), and eternal.
But "eternal" means that he lasts for ever, not that he can move backwards and forwards in time.
Your statement about angel's "habitation" implies that they exist in a finite volume of n-space and, like God, move only forward in time. Likewise, their penetration into a volume of our 3-space is a finite 3-space volume. Therefore your argument that they take up a zero 3-space volume is invalid (or 2-space, if we restrict the solution to the surface of the head of a pin). It may be at the planck scale, but it's still a volume or area.
I do agree that the finite number of angels (100+ million) provides a practical upper limit. For example, we could say (and I'm picking these numbers out of the air), that 100 Billion people could stand in a thousand-square mile area -- but the actual number is limited by the world's population.
I see no evidence that angels, NOT being omnipresent, can occupy the same volume of n-space, so the exclusion principal applies: they must occupy separate volumes in n-space and, as a sub-set, in 3-space.
Next, we come to standing or dancing. The Bible has nothing to say about whether heavenly beings dance or not, but some human dancing is endorsed (and some is declaimed.). But I cannot conceive of a heaven filled with the sound of musical instruments, and the listeners of that celestial movement being required to stand still.
In any case, you argue that the 3-D size of an angel is vanishingly small. It will most likely also be subject to a N-dimensional Heisenberg uncertainty principal. By setting their velocity to zero (no dancing) you set the uncertainty of their position to infinity, so you can no longer claim with certainty that they are ON the head of the pin.
