gosenjoyer
You realize the point of airplane mode is to disable the cellular modem (and optionally WiFi), right?
The only way to make or receive calls or SMS in airplane mode is via Voice (or SMS) over WiFi.
Your carrier needs to support that (most do, but not all). And you have to have it enabled in settings for your SIM (seems to usually be enabled automatically, but may not always).
If you think it should be working but it isn't, your best bet is probably to contact your carrier.