Hi,
I have the same problem including at Uni' But I have a fix if it helps regarding the Keynote Remote App'.
To get your iPhone and iPad working together ( so you can use Keynote Remote ) try this.
Turn off Wi-Fi on both
Go to Settings on iPhone and turn on "personal Hotspot", it will say that it wants to turn on both Wi-fi & Bluetooth, let it.
On iPad turn on Bluetooth
Back to iPhone and I turn off wi-fi only, SO you should only have on Bluetooth on both plus Personal Hotspot,
If you have Settings/Bluetooth open on both, you should see them trying to find each other, also
small Blue bar at the top of iPhone will show " Personal Hotspot connection".
On the iPad under "Devices" your iPhone name should appear, click on the name ( not Blue icon ) it will find the phone and say 'Connected" ( I hope )
Open up your Keynote Pres' on iPad, start The KN App' in iPhone and it should all work, fingers crossed.
Best of luck and I hope this helps
Let me know if you have problems.
Steve ( uk )