Answers of prayers to God, are confirmed only by 'cherry picking' the facts and then using tremendous 'leaps in logic'.
Look at all the reasons people give for believing or felt their prayers were answered by the Deity of choice. These reasons usually have a strong emotional tug and so are very subjective in nature as well as very biased based on religious conditioning/indoctrination.
So I would definitely conclude that it is definitely just 'self delusion' based on religious conditioning.
Now Synchronicity on the other hand well that is a different related subjects that I'm still trying to work out.
Synchronicity (German: Synchronizität) is a concept, first introduced by analytical psychologist Carl Jung, which holds that events are "meaningful coincidences" if they occur with no causal relationship yet seem to be meaningfully related. During his career, Jung furnished several slightly different definitions of it. Jung variously defined synchronicity as an "acausal connecting (togetherness) principle," "meaningful coincidence", and "acausal parallelism." He introduced the concept as early as the 1920s but gave a full statement of it only in 1951 in an Eranos lecture.
In 1952 Jung published a paper "Synchronizität als ein Prinzip akausaler Zusammenhänge" (Synchronicity – An Acausal Connecting Principle) in a volume which also contained a related study by the physicist and Nobel laureate Wolfgang Pauli, who was sometimes critical of Jung's ideas. Jung's belief was that, just as events may be connected by causality, they may also be connected by meaning. Events connected by meaning need not have an explanation in terms of causality, which does not generally contradict the Axiom of Causality.
In the introduction to his book, Jung on Synchronicity and the Paranormal, Roderick Main wrote:
The culmination of Jung's lifelong engagement with the paranormal is his theory of synchronicity, the view that the structure of reality includes a principle of acausal connection which manifests itself most conspicuously in the form of meaningful coincidences. Difficult, flawed, prone to misrepresentation, this theory none the less remains one of the most suggestive attempts yet made to bring the paranormal within the bounds of intelligibility. It has been found relevant by psychotherapists, parapsychologists, researchers of spiritual experience and a growing number of non-specialists. Indeed, Jung's writings in this area form an excellent general introduction to the whole field of the paranormal.
In his book Synchronicity: An Acausal Connecting Principle, Jung wrote:
...it is impossible, with our present resources, to explain ESP, or the fact of meaningful coincidence, as a phenomenon of energy. This makes an end of the causal explanation as well, for "effect" cannot be understood as anything except a phenomenon of energy. Therefore it cannot be a question of cause and effect, but of a falling together in time, a kind of simultaneity. Because of this quality of simultaneity, I have picked on the term "synchronicity" to designate a hypothetical factor equal in rank to causality as a principle of explanation.
Synchronicity was a principle which, Jung felt, gave conclusive evidence for his concepts of archetypes and the collective unconscious. It described a governing dynamic which underlies the whole of human experience and history — social, emotional, psychological, and spiritual. The emergence of the synchronistic paradigm was a significant move away from Cartesian dualism towards an underlying philosophy of double-aspect theory. It has been argued that this shift was essential to bringing theoretical coherence to Jung's earlier work.