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Yes
No. Technically they cannot. Brahmbhatt is not really considered Brahmin but a intercaste production between Brahmin and Kshatriya. Most in the Brahmin community do not consider them Brahmins even.
People of same 'gothras' marriage is not advised
Yes
can marry a boy beloging to kasyapa, dhanunjaya & koundinya gotras
can kashtriya girl can marry Rajakas boy
according to manusmriti it should not be done
Yes, ofcorse they can marry....because they both belong to Rajput community
Yes can marry. But girl can't marry any Kulin Brahmin boy due to the difference in civilization, religion. The enmity between rudraj brahmin and Kulin Brahmin developed at the time of King Ballal Sena of bengal. And also because Kulin are ethnically not Bengali ,they are from Kannauj(UP) and their real name is Kanyakubj Brahmins
cant. only if she Muslim, Jew or christian.
In Brahminical literature, marriage between Brahmin girl and Kshatriya boy is forbidden but there are some cases from ancient era which points out that marriage between Brahmin girls and Kshatriya boys were practiced and had social acceptance. For example, Marriages between Yayati and Devayani & Dushyant and Shakuntala. Well all i can tell you is that cast is nomore relevant to anything now, because shiri Krishan ji has finished it when they gave us the knowledge of Gita, now your karam is your dharam. if you are a brahmin girl think twice before you take any action cause you are considered as one who has knowledge. just have a good thought about the guy if he has any qualities of brahmin or what i mean is if he has any signs of brahmin, what i mean is if he acts like a brahmin then it is allgood because his karam is his dharam. well if he acts like a kshatriya then one of you would have to sacrifice. Pardon my spelling mistakes if you find any.
No, Because from same gotra means that you are brother & sister. Which is considered forbidden for wedding.