Mobile phones can get a signal when airborne, but only to about 4,000'. I can hear the sound of a phone trying to get a signal through my headset in the cockpit as I come into land - it is similar to noise a mobile phone can make next to television. It doesn't seem to be that common now, maybe people are obeying the rules or maybe smartphones don't make the same kind noise.
You can definately get a GPS signal when airborne. Every modern airline uses it. While we don't use it, the GPS altitude seems pretty stable.
Being slightly pedantic, there are legal reasons why you cannot use your mobile in flight.
1. All aircaft have radio licences detailing what transmitters and receivers they have - your mobile is not on that licence.
2. Pilots have Radiotelephony Operators Licences, which allow them to use said radio equipment, you probably do not.
While the risk is very small, I wouldn't like to loose all flight instruments just after take off on a dark windy night because someone left their phone one.