My impression from studying Buddhist scriptures is doctrines of reincarnation developed more & more with the advancement of Buddhist history. In the early Pali scriptures, there appears actually no word that literally means 'rebirth' or 'past lives'. For example, there appears only one sutta that explains the meaning of the term 'pubba-nivasa', which literally means 'past-dwellings' but is often translated as 'past-lives'. This one sutta is SN 22.79, which appears to explain a 'past-dwelling' is every time in the past the mind ignorantly clung to one or more of the five aggregates as 'self'. In addition, there are many suttas that appear to use the six realms as here & now mental states, such as SN 35.135.
In summary, the question of this topic sounds based in later day Tibetan Buddhism, which, similar to later day Theravada, has very structured literal doctrines of reincarnation. However, from the earlier Pali suttas, it appears a case can be made for different (here & now) interpretations of what are called 'the six realms' and 'past lives'.
As for supernormal psychic powers, the early Pali sutta report the Buddha & some (but not all) of his enlightened disciples can these. Supernormal psychic powers have no relationship to the six realms or notions of past & future lives. In the early Pali suttas, it is reported the Buddha used supernormal psychic powers to observe the (moral) rise & fall of beings according to their kamma. The Buddha did not use supernormal psychic powers to observe past-dwellings (or what is commonly translated as past-lives). This can be read in the stock phrases describing the Three Knowledges, as found at the end of MN 4 and DN 2.
"With his mind thus concentrated, purified, and bright, unblemished,
free from defects, pliant, malleable, steady, and attained to
imperturbability, he directs and inclines it to knowledge of the
recollection of past lives (lit: previous homes). He recollects his
manifold past lives, i.e., one birth, two births, three births, four,
five, ten, twenty, thirty, forty, fifty, one hundred, one thousand,
one hundred thousand, many aeons of cosmic contraction, many aeons of
cosmic expansion, many aeons of cosmic contraction and expansion,
[recollecting], 'There I had such a name, belonged to such a clan, had
such an appearance. Such was my food, such my experience of pleasure
and pain, such the end of my life. Passing away from that state, I
re-arose there. There too I had such a name, belonged to such a clan,
had such an appearance. Such was my food, such my experience of
pleasure and pain, such the end of my life. Passing away from that
state, I re-arose here.' Thus he recollects his manifold past lives in
their modes and details. Just as if a man were to go from his home
village to another village, and then from that village to yet another
village, and then from that village back to his home village. The
thought would occur to him, 'I went from my home village to that
village over there. There I stood in such a way, sat in such a way,
talked in such a way, and remained silent in such a way. From that
village I went to that village over there, and there I stood in such a
way, sat in such a way, talked in such a way, and remained silent in
such a way. From that village I came back home.' In the same way —
with his mind thus concentrated, purified, and bright, unblemished,
free from defects, pliant, malleable, steady, and attained to
imperturbability — the monk directs and inclines it to knowledge of
the recollection of past lives. He recollects his manifold past
lives... in their modes and details.
"This, too, great king, is a fruit of the contemplative life, visible
here and now, more excellent than the previous ones and more sublime.
With his mind thus
concentrated, purified, and bright, unblemished, free from defects,
pliant, malleable, steady, and attained to imperturbability, he
directs and inclines it to knowledge of the passing away and
re-appearance of beings. He sees — by means of the divine eye [supernormal psychic power],
purified and surpassing the human — beings passing away and
re-appearing, and he discerns how they are inferior and superior,
beautiful and ugly, fortunate and unfortunate in accordance with their
kamma: 'These beings — who were endowed with bad conduct of body,
speech, and mind, who reviled the noble ones, held wrong views and
undertook actions under the influence of wrong views — with the
break-up of the body, after death, have re-appeared in the plane of
deprivation, the bad destination, the lower realms, in hell. But these
beings — who were endowed with good conduct of body, speech, and mind,
who did not revile the noble ones, who held right views and undertook
actions under the influence of right views — with the break-up of the
body, after death, have re-appeared in the good destinations, in the
heavenly world.' Thus — by means of the divine eye, purified and
surpassing the human — he sees beings passing away and re-appearing,
and he discerns how they are inferior and superior, beautiful and
ugly, fortunate and unfortunate in accordance with their kamma. Just
as if there were a tall building in the central square [of a town],
and a man with good eyesight standing on top of it were to see people
entering a house, leaving it, walking along the street, and sitting in
the central square. The thought would occur to him, 'These people are
entering a house, leaving it, walking along the streets, and sitting
in the central square.' In the same way — with his mind thus
concentrated, purified, and bright, unblemished, free from defects,
pliant, malleable, steady, and attained to imperturbability — the monk
directs and inclines it to knowledge of the passing away and
re-appearance of beings. He sees — by means of the divine eye,
purified and surpassing the human — beings passing away and
re-appearing, and he discerns how they are inferior and superior,
beautiful and ugly, fortunate and unfortunate in accordance with their
kamma...
To conclude this question, which is about 'superstition', in the early Pali suttas, there is only one Dhamma Refuge, which is defined as follows:
‘Bhikkhus, this Dhamma is visible here and now, immediately effective, inviting inspection, onward leading, to be experienced by the wise for themselves.’
MN 38
