Pune Airport, India -- When to enter terminal for a 04:10am flight?

There is no such rule. It will be useful if you can share the reference article.

You can enter terminal well in advance but boarding pass will be issued when airline opens the counter. A wayout can be to generate boarding pass online or via automated machines but then if you have luggage you need to wait till airline counter opens.

In airports in India, there will be security guards at Terminal entry gates who will validate your ticket and ID proof.

I have been warned about the same 'limit' by many colleagues, but have never encountered any such check or questioning (throughout 2016 an 2017). I typically go to the airport lounges about 22:00 for 3:30 flights.

I would assume it's obsolete or an urban legend.

It depends on the security concerns of the airport. I have spend nights at T-3 (Delhi) and in one instance, slept at the boarding gate and missed my flight. At the same time, they refused my entry (about 9 hours before my flight), becuse January 26 was around the corner and security alerts were issued.

You are advised to be at airport 2 hours prior to your flight (domestic) & 3 hrs prior for international flight. In case you are early by not more than 12 hours, you can say that you are coming from a different city and reached early (used that trick once & it worked ;))

You should check with your airline, when you should go to airport. It is dependent on airline and airport, and so these rules are documented on airline website and usually also on the booking documentation.

On many airports, (some) terminals (after security check) or gates are accessible just before the departure of flight, but this doesn't mean that you should go to airport earlier for check-in.

This happens often on small airports, and sometime also on some large airports for some gates (especially for special flights, small planes or special routes).