You have to first understand that this entire scenario was over a relatively long period of time, many hours, and will have seen many feints.
When you are not at war, an attacker always has the advantage because the attacker chooses the time and place. So when the F-16s actually attacked the MKIs, the MKIs had no idea that they would be attacked. Why? Because the PAF will have launched many such "attacks" over a long period of time without actually doing anything. Imagine the two of us worked at the same office. Every time I see you, I always raised my hand in a position that is ready to slap you every time I passed by you, but I never slapped you, so you never know if I'm being serious or not. But what if one day I did slap you? And once I slapped you, it would take time for you to regain your composure again. But what happened during Balakot is, after I slapped you and you were out of the picture for a few seconds (MKI), your friend sitting in a cubicle that I didn't notice decided to fight back and took me by surprise (Mig-21).
After the F-16s (me) fired at the MKIs from their own land, the MKIs (you) went cold. At full range, the Aim-120C has 2 minutes of flight time. So, in this window, while the MKIs were escaping from the initial volley, 3 F-16s entered our airspace. Even after those two minutes are up, the MKIs still need more time to return to position and become a threat once more, which could be a minute or even two minutes. PAF expected that their 3 F-16s would have finished their task by this time and would be returning home. But they didn't expect the Mig-21 (your friend) to be around to jump on the 3 F-16s. The Mig-21s finished the work in less than 2 minutes.
As for why Abhi pursued the F-16s, it's obvious that the F-16s entered our airspace and wanted to attack us, that's why he gave chase. When the MKIs were facing the F-16s, the MKIs wouldn't have been able to tell if it was an actual attack or a feint. It was only after the Aim-120s were fired (slap) that the MKIs would realise they were under attack after all.
Firing at Dmax (full range of the missile) is utterly useless. This is even less likely to work during war, when borders become irrelevant.
You will also notice from the IAF's radar images that once they lost their F-16, the F-16 closest to the Mig-21, that was probably trying to help the F-16 that went down, went cold. So those 2 MKIs had likely become dangerous to them by then.
Obviously we do not know what the RoEs were. But there have been reports that even after the MKIs were attacked, the MKIs did not get permission to retaliate, probably because the controllers expected the Mig-21s to do the job. Also there were reports that even Abhi was asked to back off.