Windows 7 on Mac Mini (Mid-2011)

Couple guesses - for the sound via HDMI try going into Windows Sound settings (Playback devices) and then see if HDMI is listed there. You will need to set it as default.

For the screen alignment - which GPU is in your Mini? If that is ATI - download and install latest ATI driver and run the Catalyst Control Center. In the CCC utility there are options that allow you to align your screen. I believe similar utilities exist for Intel and Nvidia GPUs too.

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I use Windows Media Center and Media Browser and Media Center Master on my 2011 Mac mini 2.7GHz Dual-Core Intel i7 as the residential media gateway (hub). It feeds Xbox 360s for CableCARD DVR, music and movie libraries. I also struggled with direct output to the TV. Mainly the 29/59 frame rate issue. I suggest installing the lastest video drivers from the manufacturer, not bootcamp. Then you can align the screen there and will likely get HDMI audio without going to sound in the control panel. If necessary, go to sound and enable HDMI audio as a playback device. If you have speakers connected to the mini you will also have to enable the recorder. To enable these items you will have to show disabled devices in sound. Your TV may also have a scan adjustment. You can try setting it there as well. Often called pixel or just scan vs normal.

I followed the advice provided in this thread on AVS forum > HTPC

http://www.avsforum.com/avs-vb/showthread.php?t=1250607

After trying many variations, I ended up NOT installing the Shark007 codec pack and encoding all my movies in Handbrake Apple TV 2 preset. AVS forum tends to focus on highest possible quality. I was going for minimalist jukebox similar to an Apple TV 2, but combining CableCARD Live TV functionality. Therefore, I encode once and use on all my devices (i.e. - iTunes, Apple TV 2, iPhone 4S, iPad 2, Windows Media Center, Xbox 360). The Apple TV 2 preset has the proper bit rate, etc. for all my devices. Yes, I sacrifice some quality, but I save disk space and gain compatibility.

Windows Media Center:
My HTPC is the 2011 Mac mini 2.7GHz Dual-Core Intel i7. With 8GB of 1866MHz, SSD Windows 7 x64 OS drive recording 6 shows at once and playing back on two Xbox 360 extenders simultaneously is no problem.

Media Browser:
I use the current release 2.5.2 on my library stored on a SSD modded RAID 0 LaCie Thunderbolt Little Big Disk. It is super fast for the Media Browser library even through the Xbox 360 extenders. Media Browser is access many backdrops and posters for each movie. I also use the paid (donation supported) Neo - Metro Theme. My movies are split into HD, International, and Movies (for SD DVD backups).

Media Center Master:
I use the free version and its fine for renaming and downloading artwork. The HTPC is configured to auto resize the artwork using the default settings. This helps speed the Media Browser interface on the Xbox 360 extenders. After my initial load, I turned off auto scan and manually run the job for each movie I add. I point Media Center Master to the same directories listed above for Media Browser libraries. Before resize, I add the artwork to my iTunes Library because it can leverage high resolution than Windows Media Center. I also add the synopsis from the xml files created by Media Center Master to the description, artist (director) and year fields under get info.