I have an iPhone 5S and I am looking for a way to mirror my screen to the TV. I was wondering if I could use the hotspot on the phone to connect my PC (on the TV) and the iPhone, to airplay to the PC, which mirrors to the TV. Thank you!
Though info on the topic seems somewhat sparse, a few threads like this and this seem to indicate that using a hotspot works as a viable Wi-Fi network for AirPlay (as long as, of course, you connect both the iPhone and the computer to the hotspot.) However, if you've already got a Wi-Fi network, you'd probably be better off using that instead of a hotspot.
Since your PC doesn't support AirPlay off the bat, you'd need some sort of software like AirServer to make it a valid AirPlay device. From there, simply connect it to your TV and AirPlay from your phone to the PC.
However, if you do have an Apple TV, a feature called Peer-to-Peer AirPlay is available that will let you AirPlay from your iPhone to your Apple TV without a formal Wi-Fi network, circumventing the need to create a hotspot. Just turn on Bluetooth and Wi-Fi on both devices and it should work. Note, however, that AirServer doesn't support this, so you would need an Apple TV.