Unless you completely power off the radio you will still receive calls and messages. Some custom roms come with this option, but I don't know if it's possible to automate.
If you want to save more power, then enabling airplane mode and then turning wifi and / or bluetooth (depending on your needs) back on should save more power.
No, sorry. Airplane mode should stop all data exchange with mobile radio, but you should still be able to enable wifi and bluetooth while airplane mode is on.
I'm pretty sure all communication with carrier is disabled when airplane mode is on, which should save more power than disabling only mobile data transfer (in this case calls and messages still get transfered and connection with carrier is active).