Rashmi did handle the situation well, and Asim isn't wrong either.
This season, sanchalak has never been fair and it is used to their advantage. So it's not wrong on Asim's part saying he didn't see Vishal get off the horse. And bb cleared that the final decision is of the sanchalak.
Now rashmi didn't want to fight with Shukla and was worried about the physical violence thing after madhurima is evicted. She just want Asim to be safe, not to hurt or get hurt by the demon. She didn't want to fight with the shukli's. May be when Shukla was convincing her that Vishal got off, she should have said it's Asim's strategy. Bas!!
Coming to the fight with Paras, there is an UU where mahira was nagging Asim to clean the bathroom. When someone else can ask him about his duties, why can't he ask others to do their duties? It is not that he is supporting Rashmi alone, he was supporting himself too. BB has manipulated the situation too well by editing the part.