Mounting on a tree is not the best for the tree but would work. A 4x4 wood or a sturdy metal post the same diameter as the dish j-mount might be better. Be aware that the dish does not need to be mounted very high up, just high enough to avoid temporary obstacles such as snow drifts, vehicles, animals, humans, etc.
I usually use 1" black PVC or larger for small cables. Smaller conduit might work but conduit that is too small increases friction and the possibility of cable damage. Larger conduit may be required for more than two RG6 cables. Black PVC conduit is usually available in up to 100' coils at plumbing or building supply stores. Direct burial cable is another option but is more susceptible to physical damage.