- There are three types of devices you might want to connect via Bluetooth, being A) Bluetooth Low Energy (BLE) devices B) Classic Bluetooth accessories participating in MFi program C) some generic Classic Bluetooth devices, like hands-free headsets.
With BLE devices you can do almost whatever you want. You can get a list of them inside your app, present it nicely and let the user choose a device to connect (or connect transparently).
MFi devices you can either see in Settings.app or in Accessory Picker popup (see ExternalAccessory.framework reference for more details). However, you don't have control over the Accessory Picker. But after the user has selected the device there, you can see it programmatically as connected.
With standard Classic Bluetooth devices, like hands-frees, your one and only pairing option is to go to the Settings.app and pair from there. End of story.
So no, there's no such magic place where you can see all the devices around you. You should know in advance with which type of devices you need to communicate and react accordingly.
There's no standard framework to deal with standard Classic BT devices, different Apple frameworks are responsible for them. And in general, you can't do much, most communication is being done internally by the system. E.g. for hands-free devices you can only detect that such device was connected/disconnected (see more here).
HFP and A2DP are Classic Bluetooth profiles that have nothing to do with BLE. You can't see a list of such devices around using CoreBluetooth.framework.