I finally got the chance to take the new M11 IST airport metro line.
A few comments: trains leave from Gayretteppe at :00 :20 and :40 and from the airport at :03 :23 and :43. Such low frequency is because the line is still single track in some parts (to be rectified soon). Once the tunneling works are completed, things should improve. The line is run by TCDD (for political reasons), but that has no impact on your experience.

Gayrettepe to Istanbul Airport takes 30 min. Once the Terminal 2 station opens soon, I would add another 3-4 minutes to the ride. Gayrettepe station is 78m below surface (deepest in Istanbul) and it takes a good 5 minutes to get to the platform level from the ticket gates. Plan for a 12-15 minute transfer between M2 and M11 (you need to exit the M2 station, follow signs for Metrobüs, and 350m later you'll get to the M11 entrance), and a bit less between Metrobüs and M11.

From Haliç to the airport, plan for about 70-80 min, depending on how lucky you get with getting the M11 train.

The walk from the metro station to the IST check-in counters takes another 10-12 min.