Yes they can keep their original thoughts.
The holly Islam Book “Quran” maintains full respect to Christianity and full respect to Jesus (peace upon him) and calls for mutual respect between both religions.
Again, yes it is possible for a Christian or Jewish girl to get married with a Muslim man while both maintaining and practicing (at home and/or Church/Mosque) their own religions.
No he cannot. Only if she converts to Islam “The religion of Peace”
Hint on Answer B above: It is not licit to forbid what is allowed in Quran or allowed by Prophet Muhammad (peace upon him).
Quran says (English meaning translation):
“…. The food of those who have received the Scripture (Christians and Jews) is lawful to you, and your food is lawful to them. And so are the virtuous women of the believers and the virtuous women of those who received the Scripture before you (lawful to you in marriage) when ye give them their marriage portions and live with them in honor, not in fornication, nor taking them as secret concubines…”
(Quran, chapter 5, verse 5)
Accordingly, Answer A is the correct answer. Yes, it is allowed for Muslim man to marry a Jewish or Christian woman without religion convert.
From the Muslim point of view, it is acceptable for a Muslim man to marry a devout Christian woman (though not a woman who is only nominally Christian).
However, from the Christian point of view, such marriages are utterly forbidden. A Christian can only marry another Christian. The only way a devout Christian woman would agree to this marriage would be if the man converted to Christianity. If she agreed under any other circumstances, she would not be devout, and hence she would be forbidden to the Muslim man!