Hello,
I apologize for the delay in responding to your message (I just saw it) and for the really lackluster responses you've received.
The Otium Mobile site has a owner's manual for the Gear S - it is a PDF. That PDF contains this link:
That APK is for Android devices and won't work on iOS devices - and, really, isn't needed for iOS. Be grateful, BTNotification digs its claws deep in to Android, and it wants access to everything! There is also a 2D barcode on the watch, as an app - QuickResponse. I don't know where that will take you, but it should be a link to the app. You'd have to have a QR code reader on your Android device to use that code.
Since that APK isn't signed by anyone, you'll have to turn off the protections Android has in place to prevent malware from running before you can install it. Don't worry, it will detect these protections and walk you through disabling them.
I did install the BTNotification app and paired it with one of my Android phones - that didn't enable all the features, like the remote camera and the BT Notifications app on the Gear S. Broken? Unfinished? That's kind of the impression I am getting.
The Gear S, when paired with OS X or iOS, works well enough to do things like control what music is playing, do file transfers, etc. I don't have an iPhone, so I can't tell you whether or not it will dial and take calls. I imagine it would, much like a BMW's iDrive. That the Gear S was able to reach in to my Mac and iPod and play music of BT, channeling the sound to the Gear S's speaker, was impressive.
I use a cut-down SIM inserted in the watch and it works perfectly. Granted, the on-screen keyboard is a bit small for texts. It's a pity the device won't pair with a BT keyboard.
Whether or not an iOS app can be written to take advantage of the Gear S is something I don't know just yet. I have a couple of other projects brewing, but I figure I'll get around to playing with it eventually. At least the device isn't ignored by iOS! That's a fantastic thing!
Now, if only we could get the PS4 BT controller to be recognized. Oh, how dreamy that would be...