But in general, yes.. The card I told you to get (that specific model) has HDMI output. And as long as its plugged into an HDMI input, you will be able to display your PC on your TV screen. A lot of TV's have a limit in the resolutions they allow however, I know my brothers TV will not allow 1080p output from his PC but he plays Rappelz in 1440x768 or some resolution like that, so it's technically 720p instead.
Also a lot of cards have a special TV out mode, where its basically an overlay or whatever, and the picture is output to the TV and the signal is played back at whatever default resolution the TV defaults to / or detects the signal as capable of.. Versus displaying your PC desktop, etc on the TV like a monitor and blowing up a video file to full screen, etc.. That may get you crappier quality unless the video is actually encoded at the resolution you are displaying.. Ie if its a 1080p resolution (Whatever x 1080 pixels) and you don't technically need to stretch the video, etc in the player then it should playback fine with full quality, just go to full screen mode to hide your desktop etc.. Make sure the player is set NOT to stretch the video, and to maintain its original aspect ratio.
I hope I'm not confusing you.. I honestly don't know much about this stuff, but have a very basic understanding of how its supposed to work.
Should display fine.
As far as getting HD sound... If you have a home theater receiver that has the older style RCA input jacks for each channel.. (Basically a shitload of jacks on the back, a left / right RCA jack for - Fronts, Centers, Rears, and a subwoofer output, etc) then you can get full 5.1 surround sound (assuming the MKV's audio track is 5.1 and not stereo) by using several different methods..
Creative sells a cable (I have two sets) that plug into the speaker jacks on my X-Fi Xtreme Gamer card.. color coded just like actual PC speakers.. I plug in the 3.5mm Front, Center/Sub, and Rear jacks to the soundcard.. and on the other end of the cable are RCA plugs, with enough of them to create 7.1 surround if your receiver supports it (Side L/R these go bewtween the front and rear speakers in the room) or leave out the side speakers, and connect it in traditional 5.1. So you can game in 5.1 on your home theater, or upmix your music to 5.1 w/the sound cards tools, or even if you watch a 5.1 sound movie, it will all come through in 5.1 sound to the receiver because of the cable and not be a "fake" mode that the receiver often comes with to make virtual surround.
And no SPDIF /Optical TOSLINK cable is involved.. CCCP (the codec pack I recommended) comes with a tool that lets you setup your mixing of sound too.. So it can handle 5.1 soundtracks in MKV's etc.. Even if they are AC3 encoded (Dolby Digital, DTS, etc).
But the mixer also has the option (and your sound card might too I think) to pass the 5.1 signal "through" using SPDIF so the signal goes to your receiver and the receiver decodes it, just like would happen with a DVD player sending the signal to the Receiver.
So there are many options for getting real surround / hi-def sound on your system..
Because one day I will buy a TV specifically to be used for TV, DVD, consoles, AND PC gaming.. I will invest in a receiver that has 5.1 or 7.1 channel RCA inputs on the unit, so I can use the cable if I need to.. Hopefully soundcards that work as they do now, but encode sound to a Dolby signal on the fly and output it via SPDIF/Optical for receivers, will be around and affordable for the average joe.. Then you wouldn't need all the RCA hub-bub and special cables..
Even if you are using onboard sound, and not a creative sound card, I think the cable can still work (we tried it on my brothers receiver, with his onboard chipset, but couldn't get the channel just right - this may have not been the cables fault though).