This evergreen, spreading shrub growing over large boulders has been there as long as I can remember but I don't recall ever seeing it flower and no fruit is apparent. The flowers may be very small or hidden by the foliage. Either way, they don't seem to be a feature. The effect is a little bit like a prostrate Pieris but I doubt that's what it is. The toothed leaf edges and red new growth are reminiscent of Photinia but without any flowers to help I just don't know
Yes, it looks quite like Pieris japonica - maybe a dwarf seedling that has not been widely propagated and dispersed. One of partly similar character that is well-known is 'Little Heath Green'.
Yes, 'Little Green Heath' does look quite a bit like it, but not so definitively that it couldn't be something else.