Is Shakha-Bhed (inter-Shakha) marriage prohibited? If yes, then explain why and where is it mentioned? Can a Rigvedi Brahmin marry a Yajurvedi Brahmin?
I'm not aware of any such restriction.
Shakas (and most other Vedic traditions) are the son's responsibility to carry out, not daughters, because that is how lineage propagates.
If a Rigvedi brahmin man marries Yajurvedi brahmin woman, then the Rigveda tradition is continued by that couple. If it is Rigvedi woman and Yajurvedi man, then Yajurvedi tradition is continued.
Also, once a brahmin completes study of his birth-Veda, he can study the other Vedas.. so they are not prohibited from learning other Vedas, hence I don't see why they would be prohibited from marrying women born in families whose birth-veda is different.
Some of the information contained in this post requires additional references. Please edit to add citations to reliable sources that support the assertions made here. Unsourced material may be disputed or deleted.