As for Lakshman rekha, no it's not a part of Valmiki Ramayana, and neither do I think it is necessary to show it, but it's one of those stories that has become so intrinsic in Ramayana, people would find it odd if it was left out. Personally, I would not mind if it was left out.
In Valmiki Ramayana, Ahalya is not such an innocent character. She knew Indra had come as Gautam rishi to her, and she knowingly committed adultery out of curiosity and desire.
Yet, society as a whole views her as an abla naari. They think of her as totally innocent and Gautam rishi as the villain in her life.
Ahalya being shown as an innocent woman is the version every single show and movie follows.
Likewise, Lakshman rekha has become intrinsic to Ramayana, but it's not there in the original version.