On the question about Kush & Luv after Rama left for Vaikuntha
First of all, from a historical perspective, given that quite a bit is known of Kush but nothing of Luv, I don't buy the theory that Kosala was split between the 2, or else, there would have been 2 dynasties. Remember - Kosala was the name of both Dasharath's kingdom and the kingdom Kaushalya originally came from. In Valmiki Ramayan, there is a mention of her brother Bhanuman. Assuming that he ruled as long as Rama did, it's possible that he had no successors, and so Luv was sent to inherit his kingdom. Which would explain why nothing is known of him, even though Kush's dynasty seems well tracked. (Tulsidas has it that Luv founded Lahore, but given that that this was a part of Gandhara, which was under Taksha, it's very much doubtful.)
When Rama departed for Vaikuntha, all his subjects left with him (undeserved IMO, given their horrendous treatment of Sita, they simply didn't belong there). So Kush was crowned ruler, and led expeditions in the Vindyas, and established a city called Kushavati and made it his capital. He married a Nagakanya named Kumudhati - sister of a Naga ruler Kumudh - and with her, had a son Atithi, who succeeded him and continued the dynasty.
What I am also interested in is what became of the other dynasties in Raghukul - the ones of Subahu, Shatrughatee, Chandraketu, Angad, Taksha and Pushkal - sons of Shatrughan, Lakshman and Bharat, in that order? Any sources that shed light on this?