iSkysoft video converter does the job.
Also you could consider buying a cyclone HD enclosure from Sumvision - this is what I have my MKV's on and play them through HDMI on the TV.
I have used handbrake to convert MKV files its worked good so far, i usually convert to quicktime though not avi, i believe handbrake has an option for avi as well.
Yes it may well do, but it's dreadful, and is seriously dodgy.
There are many ways of playing MKV on your TV, that's not what was asked though.
Right, for that I imagine it's fine then, as ultimately quality isn't a great issue I guess.
Interesting that you use it for filmed HD content too.