There are other devices that can airplay too… but yes - you won't see the AirPlay icon unless there's a device capable of being AirPlayed to on the network.You won't see the airplay icon unless there is an Apple TV device nearby while the phone is on wifi.
AirDrop did not load for me either when I updated to iso7. I just updated to iso7.1 and had hoped that would solve it , but it did not. I have been right next to someone with another iPad and they had airdrop , so I know where it is in the control center and I know that I have to be near another wifi device with airdrop, but it is not in my control center and have not been able to send or receive via airdrop. Any suggestions?