Ayaan's actions or words can't be justified and now the damage is already done. In this situation should he give up and say, "I have done mistake, I am not worthy of Faltu, go Faltu live ur life"? No, this is Ayaan my friend! He will make the world up-side down to achieve what he wants. Only sane thing to do is, damage control.
What I understand from his current Romeo behaviour or his attempts to prove his love for her is that he knows he can't win Faltu's trust in one day. So to execute his plan he can attempt two things: first, to bring Faltu close to him by any means and make her realize that he loves her or vice versa, as that is Faltu's only weakness. Second, with time, he can win her trust back, as winning trust is a lengthy process. Ladka chalak hain!
Ayaan's trust didn't break in one day; with a series of misunderstandings, he started to doubt her. Similarly, it will take time for Ayaan to regain Faltu's trust. Can he do that? Only time will tell.