This is a bit of a knotty subject - there are two named 'disorders' that cause oddly mutated flowers or stems; one is fasciation, and the other is proliferation. The latter usually only affects the flowers, but sometimes there is evidence of fasciation in the stem as well, whereas fasciation usually affects stems, but also can affect flowers. On examining that mutated flower in your top picture, it does appear almost as if one, two or three flowers have appeared in the same flowerhead causing this odd looking flower, with no apparent fasciation of the stem, in which case, it's more likely proliferation - but the dividing line is a grey area!
The cause is essentially the same in both conditions; it's a mutation caused by a disturbance or break in the genetic code. As to what causes that, it might be weather conditions at the time the growing tip or flower was just beginning to form, viral, bacterial, physical damage, or simply an internal genetic DNA blip. It generally occurs on just the one flower (but not always) and subsequent flowers are perfectly normal, but the phenomenon may be more common on some plants than others - some roses varieties can be more prone to proliferation. Info on Fasciation https://www.rhs.org.uk/advice/profile?pid=525 and more on Proliferation https://www.rhs.org.uk/advice/profile?PID=634