No, no, mobiles don't work out at sea or at high altitude. I don't imagine there are many cellphone masts along the Malaysian & Indonesian coastlines, tbh, it's mostly jungles & mountains - and if the plane flew low to avoid radar, it would have avoided any mobile signals as well!
There aren't any cellphone masts in the middle of the Indian Ocean. The passengers making calls on 9/11 were flying low over New York. New York has lots of cellphone cover.
... some long-haul planes now provide mobile data connection for a hefty price. The price is hefty because the signal has to be relayed thousands of miles via the plane's radio system, bouncing off satellites & being routed by ground stations to get to a cellphone service.