I think I have answers for you - but I am going partially by memory and that is not 100% trust-able. Someone correct me if I am wrong please. I just added the tranny cooler a few weeks ago.
I'm pretty sure you can use whatever cooler model you want as long as it fits and does the job. I'd make sure someone with an Armada or Titan has used the same model. If nobody ever used it you are either off track or breaking new experimental ground.
Because there is a breather hose on the tranny I don't think air in there is a problem. I didn't even consider it.
The ID of the tranny hose is 5/16. I used this -
Make sure you get TRANNY hose - not something made for something else.
I also used these hose clamps someone here recommended - they are nice.
The capacity of the cooler is pretty small. Almost none leaked out when I installed mine and after install the dipstick showed no need to add any more fluid. I checked again a few hundred miles later and it was still good. So I'd guess the volume is negligible or similar to the stock internal cooler we are bypassing.
Mount the new cooler first. That is what took me the longest to do - bending and adjusting the brackets, drilling holes etc.
Then take 5 min to just lay under there an ID all the hoses - figure out which goes where.
As for hose routing - (here is where my memory may be off) - the drivers side of the hard tranny line (the one with a slight angle and the end that points towards the drivers side tire) is the OUT from the tranny. Remove the hose from the end of the hard line from the tranny and where it connect to the drivers side of the radiator.
That makes the passenger side the RETURN line from the coolers. Leave this hose attached (or replace hose if you are replacing hoses) to the hard line that returns to the tranny. But disconnect the other end - where it comes from the stock radiator cooler (to then go back to the tranny in stock configuration).
Disconnect both ends of the hose that leaves the passenger side of the radiator. This should be a short piece. Cap both radiator stubs or connect them with a short hose and clamp both sides. I used the caps that were on the new cooler.
The routing I then used is - Drivers side tranny hard line (OUT of tranny) - new hose/clamp over towards the passenger side of the radiator - connects to the hard line that goes IN to the stock cooler (it runs up the pass side of the radiator). Where the pass side radiator out hose used to connect.
So now you are going out of the tranny, bypassing the stock radiator and going straight IN to the stock tranny cooler.
From there you need to find the line that comes OUT of the stock cooler (pass side of radiator) and USED to go back to the tranny. You want to connect that line to the (I used) drivers side of the new tranny cooler.
Then connect the pass side of the new tranny cooler to the hose you left attached to the return line back to the tranny.
And you're done. Some hoses were reusable but I don't remember which - but you don't need much new hose.