I bought some map apps which don't use cell data, I turned data off, no wifi it works great. But if I put it to air mode, the GPS is very slow. How can those app use my cellphone to decide the position but doesn't need cell data?
It uses a GPS chip, information from the location of WiFi sources and what's referred to as AGPS which, in general, is not as accurate and somewhat slower than what you would have otherwise. With data on, your accuracy and speed improves because you also use the Cell tower triangulation. (this is kind of a simplified answer and not entirely accurate, but it gives you the basic concept)
I found even turn data & wifi off it will be very quick and accurate. If turn to air mode, it will be slow.
In airplane mode, everything is turned off, even GPS, read the support page here:
Also, AGPS is not wifi triangulation. AGPS is assisted GPS which uses cell towers to speed the time it takes to get a GPS fix.
If what you want is to save battery and not use data, turn off Wifi and Bluetooth on the first page of settings, then go to General, cellular and turn off cellular data