There are restrictions on Airplay in Mountain Lion. It has to do with your video card that comes on the machines that you are using.
Your video card has to be powerful enough to do all the heavy lifting of streaming so that your CPU is unhindered and therefor you can smoothly still use your machine.
This question and answer should help you out and explain things and find an alternative, such as AirParrot.
Here is an Apple Support Article on the subject, listing the restrictions and giving more information on how Airplay Mirroring works.
Here is the excert from the article showing the compatible computers:
iMac (Mid 2011 or newer)
Mac mini (Mid 2011 or newer)
MacBook Air (Mid 2011 or newer)
MacBook Pro (Early 2011 or newer)
As for a Mac Pro, they are not listed as a compatible model that supports Airplay Mirroring, as discussed in this article here.
You can still connect a cable and mirror in that sense, that has not changed in ML. The mirroring feature of using a separate display is a completely different process than Airplay Mirroring.
I hope that this answer helps you out.
MKV and MP4 are not video format, they are containers. An MKV can contain any type of video/audio stream.
Most of the time, MKV contains H264/AC3 DTS (video/audio; the most common format in blu-ray).
The official specification of MP4 do not allow the AC3 format for the audio channel, but the H264 format is possible for the video. Thus, you can convert losslessly an MKV to an MP4, for the video channel only. The audio channel will have to be re-encoded
I recommend using ffmpeg (a command-line tool) to achieve this goal.
Note: You can try and create an MP4 containing AC3, but I don't think it will work in iTunes or the Apple TV, even though players like MPlayerX or VLC will be able to play them.
Best Answer
Yes.
iPhone will airplay to the AppleTV which can select the HomePod(s) as the audio from AppleTV.