Lets say for argument's sake that Arjan happens to be the real son of DM. Then what would become of Khemi's marriage to him? She will end up being her husband's maasi, wouldn't she? The whole purpose of avoiding a marriage with Hiten would then be purposeless. As the marriage happened before this relationship was known, would it make the marriage more socially acceptable or would it be declared null and void? What if there is a child in the process? Some things can really get grey that it is very difficult to make out what is right and what is not.
As to Khemi living in DM household, I wouldn't be surprised if this happens because this is a BT show and we all know from past experience that in their shows, all characters that matter live under the same roof irrespective of why and whereforth. For example, in Kayamath, the exes of the leads lived in the same house, even though there was no justification for their existence there. I think it is to do with cost cutting. If they show them living in different households, then they will have to spend more on the sets. Wouldn't be surprised to see Kanji also moving in with the Mahiyavanshis in future.