In addition to the above. I myself also have an apple tv and an ipad, an ipad mini and an iphone. Here are my own answers to your questions.
1: ipad ios 6.1, ipad mini 6.1, apple tv 5.2
2: ipad 2 64 gb, ipad mini 16gb, apple tv 3rd gen.
3: ipad's are wirelessly connected, apple tv is connected with ethernet cable, all to an apple time capsule.
4: I do have iTunes match, before and after updating (for more than a year now)
5: no issues at all, it all connects as usual, like it did before all the updates.
6: also iphone 5 on ios 6.1 connects as usual, no problem at all, never had any oroblems connecting.
With me all devices are working and have always worked. I myself did not have any connection problems with the remote app on any device.
Hope this helps, and hope you can solve the issue for my brother fast.