IOS – Why are iPhone4 and iPhone5 (iOS 7) not recognizing bluetooth devices

Provided you have done what Vlad said (enable the Bluetooth sharing) and paired the devices (which you seem to have done), I have absolutely no problem to send files via bluetooth using my Nexus-S. I have ICS 4.03 now, but I had 2.3.x (where X is 3, 4, 5 and 6 if I'm not mistaken).

Once you have the devices Paired, if the Mac is in range and with BT enabled, the phone can send files because the Mac should be on the phone's list of paired devices. I recall that in 2.3.x sometimes it won't work, but retrying to turning on/off BT was usually enough. I don't use it a lot, but I just tried (after months of probably never touching bluetooth on either device) and I got this:

Here's my preference pane:

and Finally, this is my Phone's paired list (two are intentionally blurred), but you can see my Macbook Air:

Hope you can double-check your settings.

For reference:

1. I have Firewall ON
2. I have Firewall Stealth ON.

Here's my Firewall Screen (app list blurred by me):

Yes, airplane mode shuts down the radios that amplify all antenna circuitry. Compass isn't affected by airplane mode other than not being tuned by GPS location. Your observed relative changes will be mostly unaffected but absolute accuracy could suffer between one and ten degrees on much of the globe.

Of course the GPS signals still hit the iPhone case and antennas, just the hardware doesn't do the work to fix a location from those signals while in airplane mode. (Nor does e software do any processing of the location updates which is a big part of the functionality for many people as opposed to the hardware side of the radios being idle / off / silent)