I knew it! I found the answer in the suttas!
Is such a belief/view a result of craving for views regarding rebirth?
Yes. A belief in no rebirth is a result of craving, which was also confirmed by the Buddha in this sutta:
74."There are, bhikkhus, some recluses and brahmins who are speculators about the future, who hold settled views about the future,
and who on forty-four grounds assert various conceptual theorems
referring to the future. And owing to what, with reference to what, do
these honorable recluses and brahmins frame their speculations?
84."There are, bhikkhus, some recluses and brahmins who are annihilationists and who on seven grounds proclaim the annihilation,
destruction, and extermination of an existent being. And owing to
what, with reference to what, do these honorable recluses and brahmins
proclaim their views?
85."Herein, bhikkhus, a certain recluse or a brahmin asserts the following doctrine and view: 'The self, good sir, has material form;
it is composed of the four primary elements and originates from father
and mother. Since this self, good sir, is annihilated and destroyed
with the breakup of the body and does not exist after death, at this
point the self is completely annihilated.' In this way some proclaim
the annihilation, destruction, and extermination of an existent being.
103."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.
114."When those recluses and brahmins who are annihilationists proclaim on seven grounds the annihilation, destruction, and
extermination of an existent being —
115."When those recluses and brahmins who maintain a doctrine of Nibbāna here and now proclaim on five grounds supreme Nibbāna here and
now for an existent being —
117."When those recluses and brahmins who are speculators about the past, speculators about the future, speculators about the past and the
future together, who hold settled views about the past and the future,
assert on sixty-two grounds various conceptual theorems referring to
the past and the future — 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 the belief in no rebirth comes from craving. Whoever has the described view of no rebirth is immersed in craving. It's confirmed by the sutta.
At last, I'm not insane. Now it's confirmed also from the scriptures,
that a belief in no rebirth is coming from craving!
I bow to the all knower, the Buddha.
Please note that this does not mean that the self or being continues to exist after death. This belief/view of existence after death falls under the other extreme, which is eternalism, which too must be avoided. I'll address this in the answer to this question Questions about strong acceptance of rebirth? .
Furthermore, I also found this sutta (PLEASE NOTE: for clarity purposes I'm quoting only the parts of the sutta where the belief in no rebirth is mentioned):
Bhikkhus, there are certain recluses and brahmans who declare views
about the future. Such as ... the annihilation, destruction and the
non existence of the conscience. ...
Those recluses and brahmins, who declare the annihilation, destruction
and the non existence of the conscience, fear the self loathe it, and
run round that same self. ... those recluses and brahmins, who declare
the annihilation, destruction and the non existence of the conscience
of the person, fear the self, loathe it, and run round that same self.
This is compounded and coarse ...
Whoever recluses and brahmins declared views about the future did so
declaring one or the other of the [above]. ...
There are recluses and brahmins who declare views about the past such
as .... the self and the world are not eternal, this only is the
truth, all else is false. ... The self and the world are limited ...
this only is the truth all else is false. ...
Bhikkhus, the recluses and brahmins who bear the view [']the self and
world is not eternal ... limited ... 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
Is it possible to attain Nirvana with such a belief/view?
No. In order to attain Nirvana, this belief/view must cease.
Once Nirvana is attained and after, this belief/view will cease. Why? Because when Nirvana is attained, craving ceases. Since the person who has this belief/view was immersed in craving, and this craving ceased, the belief/view will cease too and right view will arise.
Nirvana is attained when craving is eradicated. Craving is eradicated when ignorance is eradicated. Thus, one must eradicate ignorance in order to eradicate craving. This same eradication of craving is Nirvana, which is attained by the arahat.
Does an arahat strongly believe in no post-mortem rebirth and strongly deny the possibility of the existence of rebirth?
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 believe in no post-mortem rebirth and strongly deny the possibility of the existence of rebirth.
Furthermore, the Buddha said that anybody who strongly believes in no post-mortem rebirth and strongly denies the possibility of the existence of rebirth is immersed in craving. Somebody who is immersed in craving is not an arahat. An arahat has eradicated craving.