I have update to iOS 7. A number of free software is available from the App Store. Mainly business related. Trial versions include Parallels Access which enables you to remote into your Mac and/or Windows computer(s) so that you can do work away from the office (similar to GoTp My PC), or a Virtual desktop Cloud based Windows desktop software which includes the latest Office Suite. There is also Google utility Talkatone which is basically a VOIP phone. Alternatively you can use Skype and there is a built in FaceTime (similar to Skype but only apple products).
Maybe you'll get a more definitive answer. Mine is not called iPad Air but it does have a airdrop which give you various capabilities. mine has the AIRDROP capabilities which I prob don't use for max efficiency. If that what she means by iPad air and what you are referring to you're prob ok. Go to Apple support and then IOS-Using Airdrop. That what I have.
You don't need a wireless carrier (i.e. Verizon, AT&T. T-Mobile, etc.) if you only want to use the Wi-Fi. But if you choose to keep your device on a network at all times, not just when you can find a Wi-Fi network, you would need to pay their monthly fee for the data services.