1a. Is strong acceptance of rebirth in the above scenario, a result of craving? Why?
Yes. A strong acceptance of rebirth is a result of craving, which was also confirmed by the Buddha in this sutta:
30."There are, bhikkhus, some recluses and brahmins who are eternalists, and who on four grounds proclaim the self and the world
to be eternal. And owing to what, with reference to what, do these
honorable recluses and brahmins proclaim their views?
"He speaks thus: 'The self and the world are eternal, barren,
steadfast as a mountain peak, standing firm like a pillar. And though
these beings roam and wander (through the round of existence), pass
away and re-arise, yet the self and the world remain the same just
like eternity itself.
38."There are, bhikkhus, some recluses and brahmins who are eternalists in regard to some things and non-eternalists in regard to
other things, and who on four grounds proclaim the self and the world
to be partly eternal and partly non-eternal. And owing to what, with
reference to what, do these honorable recluses and brahmins proclaim
their views?
"Herein, bhikkhus, recluse or a certain brahmin is a rationalist, an
investigator. He declares his view — hammered out by reason, deduced
from his investigations, following his own flight of thought — thus:
'That which is called "the eye," "the ear," "the nose," "the tongue,"
and "the body" — that self is impermanent, unstable, non-eternal,
subject to change. But that which is called "mind" (citta) or
"mentality" (mano) or "consciousness" (viññāṇa) — that self is
permanent, stable, eternal, not subject to change, and it will remain
the same just like eternity itself.'
51."This, bhikkhus, the Tathāgata understands. And he understands: 'These standpoints, thus assumed and thus misapprehended, lead to such
a future destination, to such a state in the world beyond.' He
understands as well what transcends this, yet even that understanding
he does not misapprehend. And because he is free from misapprehension,
he has realized within himself the state of perfect peace. Having
understood as they really are the origin and the passing away of
feelings, their satisfaction, their unsatisfactoriness, and the escape
from them, the Tathāgata, bhikkhus, is emancipated through
non-clinging.
105.Therein, bhikkhus, when those recluses and brahmins who are eternalists proclaim on four grounds the self and the world to be
eternal — that is only the feeling of those who do not know and do not
see; that is only the agitation and vacillation of those who are
immersed in craving.
106."When those recluses and brahmins who are eternalists in regard to some things and non-eternalists in regard to other things proclaim
on four grounds the self and the world to be partly eternal and partly
non-eternal — that too is only the feeling of those who do not know
and do not see; that is only the agitation and vacillation of those
who are immersed in craving.
Source: http://www.accesstoinsight.org/tipitaka/dn/dn.01.0.bodh.html
Thus, from this sutta it's evident that strong acceptance of rebirth (belief that rebirth never ends or that existence lasts forever) comes from craving. Whoever has the described view of rebirth is immersed in craving. It's confirmed by the sutta.
Please note that this does not mean that the self or being is annihilated after death. This belief/view of annihilation (non-existence) after death falls under the other extreme, which is annihilationism, which too must be avoided. I addressed this in the answer to this question Is the belief in no rebirth conditioned by craving? .
Furthermore, I also found this sutta (PLEASE NOTE: for clarity purposes I'm quoting only the parts of the sutta where the belief in eternal rebirth is mentioned) which says that strong acceptance of rebirth should be given up:
Bhikkhus, there are certain recluses and brahmans who declare views
about the future. Such as there will be a healthy perceptive self
after death. ... an immaterial self, or ... a self that is material
and immaterial, or ... a self that is neither material nor immaterial
...
The Thus Gone One knows those recluses and brahmins who make known a
healthy perceptive self after death, declaring of, a material self or
an immaterial self, or a self that is material and immaterial, or else
a self that is neither material nor immaterial ... whether material or
immaterial ... He knows ... that these are compounded and coarse ...
knowing the escape from this, the Thus Gone One overcame them.
There are recluses and brahmins who declare views about the past such
as .... the self and the world are eternal, this only is the truth,
all else is false. ... The self and the world are unlimited ... this
only is the truth all else is false. ...
Bhikkhus, those recluses and brahmins who declare the view, 'the self
and the world is eternal, this only is the truth, all else is false.'
That they should by themselves realize this pure view without a faith,
a liking, hearsay, careful thinking and without a pleased view is not
a possibility. ...
Bhikkhus, the recluses and brahmins who bear the view ... [']the self
and world is eternal ... unlimited ... this only is the truth, all
else is false['] That they should by themselves realize this pure view
without a faith, a liking, hearsay, careful thinking and without a
pleased view is not a possibility.
Bhikkhus, a certain recluse or brahmin gives up views about the past
and future, not intending any sensual bonds, abides in joy secluded,
thinking this is peaceful and exalted. .... In the same manner a
certain recluse or brahmin gives up views about the past and future,
not intending any sensual bonds, abides in joy secluded, thinking this
is peaceful and exalted. ...
Source: http://awake.kiev.ua/dhamma/tipitaka/2Sutta-Pitaka/2Majjhima-Nikaya/Majjhima3/102-pancattaya-e.html
2a. Is strong acceptance of rebirth in the above scenario, a result of nihilistic ("non existence") and/or eternalists ("existence") views? Why?
Eternalists views. Because it's a view about never ending existence.
3a. Is strong acceptance of rebirth in the above scenario, a result of a view regarding self ("I have a self" and/or "I have no self")? Why?
Yes. In question 1a we already concluded that a strong acceptance of rebirth is a result of craving. Whenever there is craving, there is also becoming:
Dwelling at Savatthi. There the Blessed One said to the monks: "In one
who keeps focusing on the allure of clingable phenomena (or: phenomena
that offer sustenance = the five aggregates), craving develops. From
craving as a requisite condition comes clinging/sustenance. From
clinging/sustenance as a requisite condition comes becoming. From
becoming as a requisite condition comes birth. From birth as a
requisite condition, then aging & death, sorrow, lamentation, pain,
distress, & despair come into play. Such is the origin of this entire
mass of suffering & stress.
Source: http://www.accesstoinsight.org/tipitaka/sn/sn12/sn12.052.than.html
4a. Can an arahat strongly accept rebirth, just like person X in the example above? Why?
No. Why? An arahat knows that rebirth has ended, but for not yet liberated beings rebirth continues. That's why an arahat can't strongly accept never ending rebirth. He knows that rebirth can come to an end.
Furthermore, the Buddha said that anybody who strongly accepts rebirth by denying the possibility of ending rebirth (eternalism) is immersed in craving. Somebody who is immersed in craving is not an arahat. An arahat has eradicated craving.