The "proof" is in the Gospels and the witness of the Church. You either accept it or don't.
That blasphemy about Mary being raped is a smear that appears to have started with the 2nd century Greek philosopher, Celsus, in his anti-Christian polemics. It was repeated by Jews later with the Talmud and some other writings. The Talmud has a number of insults and blasphemies against Christ besides that. However, there's debate as to whether the Talmud is actually referring to the Jesus of Christianity or other people with the same name. So it depends on which Jews you're talking to there. I've come across Jewish people with either view. Either way, it's not taken seriously by scholars.
Tiberius Julius Abdes Pantera - Wikipedia
Oh, and the Immaculate Conception refers to Mary's conception without original sin, not Jesus. I wish people would get that right.
Yes that was a late invention.
Virgin births to world saviors was a myth in the Persian religion and the Israelites were exposed to it during the 2nd Temple Period, starting around 500 BCE. As did many of the NT stories and beliefs about God and satan.
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Virgin born
An important theological development during the dark ages of 'the faith concerned the growth of beliefs about the Saoshyant or coming Saviour. Passages in the Gathas suggest that Zoroaster was filled with a sense that the end of the world was imminent, and that Ahura Mazda had entrusted him with revealed truth in order to rouse mankind for their vital part in the final struggle. Yet he must have realized that he would not himself live to see Frasho-kereti; and he seems to have taught that after him there would come 'the man who is better than a good man' (Y 43.3), the Saoshyant. The literal meaning of Saoshyant is 'one who will bring benefit' ; and it is he who will lead humanity in the last battle against evil. Zoroaster's followers, holding ardently to this expectation, came to believe that the Saoshyant will be born of the prophet's own seed, miraculously preserved in the depths of a lake (identified as Lake K;tsaoya). When the end of time approaches, it is said, a virgin will bathe in this lake and become with child by the prophet; and she will in due course bear a son, named Astvat-ereta, 'He who embodies righteousness' (after Zoroaster's own words: 'May righteousness be embodied' Y 43. r6). Despite his miraculous conception, the coming World Saviour will thus be a man, born of human parents, and so there is no betrayal, in this development of belief in the Saoshyant, of Zoroaster's own teachings about the part which mankind has to play in the great cosmic struggle. The Saoshyant is thought of as being accompanied, like kings and heroes, by Khvarenah, and it is in Yasht r 9 that the extant Avesta has most to tell of him. Khvarenah, it is said there (vv. 89, 92, 93), 'will accompany the victorious Saoshyant ... so that he may restore 9 existence .... When Astvat-ereta comes out from the Lake K;tsaoya, messenger of Mazda Ahura ... then he will drive the Drug out from the world of Asha.' This glorious moment was longed for by the faithful, and the hope of it was to be their strength and comfort in times of adversity.
Just as belief in the coming Saviour developed its element of the miraculous, so, naturally, the person of the prophet himself came to be magnified as the centuries passed. Thus in the Younger Avesta, although never divinized, Zoroaster is exalted as 'the first priest, the first warrior, the first herdsman ... master and judge of the world' (Yt 13. 89, 9 1), one at whose birth 'the waters and plants ... and all the creatures of the Good Creation rejoiced' (Y t 13.99). Angra Mainyu, it is said, fled at that moment from the earth (Yt 17. 19); but he returned to tempt the prophet in vain, with a promise of earthly power, to abjure the faith of Ahura Mazda (Vd 19 .6)
Mary Boyce, Zoroastrianism, It's Beliefs and Practices