How can I call/message on iPad air with SIM? I have purchased an iPad Air with cellular but I cannot send and receive messages.

The name of the SIM company has appeared and I have connected it with my router. There is no icon for calling either, just an icon for messages.
You can't without jailbreaking. The SIM for the iPad air is for the data network only. You can't make or receive phone calls, nor send or receive SMS/MMS messages.