I haven't heard of too many 2010 mdx's with transmission problems. It was mainly the 2001-2006 years that had the problem and you'd have to replace the trans. The 2010-2013 mdx's do however burn oil, there's a few threads on it here if you look around. 2007-2009 years don't seem to burn oil, but the 2010-2013 years do. In the end though, the 2nd generation of mdx's (2007-2013) are pretty reliable and you shouldn't have too many problems.
There was a TSB for a 6AT reflash for the 10-11 MDX. I had the reflash done on my 11 MDX and it shifted much better and I saw a slight improvement in hwy mpgs. I think the 12-13 MDXs already have the reflash done. I don't know how you would check for the reflash other than from the Acura service records? The 6AT is the one transmission Acura has gotten right from the start. Too bad it didn't last long and was replaced with the 9AT on the next gen MDX because the 6AT was really as reliable as the the rest of the vehicle.
I use about 2/3 to 3/4 of a quart of oil during my 7500 mile oil change intervals. Not sure how to check if the 2010 is burning oil other than a +5000 miles test drive. I'm fine with my little oil burn and it hasn't caused any other problems with almost 85,000 miles on the odo.
I would be much more concerned about oil consumption. Ours has 55k and has been meticulously maintained with a 5k OCI. Oil consumption has been slowly increasing and just burned 1 qt in 4.4k miles so I changed oil. I refuse to add a quart of fresh oil when I am that close to a change. You are right to be concerned about the torque converter. Be prepared to to do an ATF drain/fill every 15k miles.