Can I use my hotspot on my phone for Airplay?
Yes.

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.