I will take a two domestic flights, from Varanasi to Mumbai then from Mumbai to Kochi. How much transfer time do I need? Will the flights be commonly delayed?
From expertflyer, the minimum connecting time (MCT) for domestic to domestic flights is nominally 30 minutes. Air India flights have a range of MCT from 0:45 up to 2:00 depending on arrival and departure terminal and flight number. Indigo has an MCT of 1 hour.
To see the typical delay, you could look up the flight numbers on flightstats. Taking a sample VNS-BOM flight AI696, it shows a poor on-time rating of 0.6 out of 5 with an average delay of 32 minutes. Today's flight arrived 65 minutes late. This flight could connect to AI681 BOM-COK with a 90 minute layover. Today, AI681 departed 49 minutes late and arrived 41 minutes late. It has an on-time rating of 2 out of 5 with an average delay of 22 minutes.
Similarly for Indigo 6E 223, BOM-COK, flightstats shows an on-time rating of 4.9 and average delay of 9 minutes. 6E 711 VNS-BOM shows on-time performance of 3.6 our of 5 with an average delay of 28 minutes.
If you search for flights from BOM-COK on Matrix or you'll see there are typically only two Air India flights per day, and only one flight per day from VNS-BOM.
It would be advisable to use the above sites to research your flights and delay performance if you have a tight connection.
If you bought a single ticket and missed your connection, the airline would rebook you on the next flight available, but this is very likely to be the next day.