Do NOT mix tires in Dual application. More info HERE
If your old tires still have lots of tread you should be able to avois the $10.50 disposal fee and generate som income from a local trucker who will grind the tires down in a year. You might sweeten the deal with the un-used tire and keep one of the used tires as a spare.
Bolt in valves cost a couple of bucks ea so $11 is a bit much other than it includes a minute or so labor. Be sure you are getting stems intended for dual application so you can easily get air chuck and pressure gauge on both rear tires.
You can probably just go with Front tire balancing.
Did someone do a dismount inspection on the dual that was next to the one that failed? You probably ran it 100% overloaded for some number of miles.