When you do a dust, you knock the guy up in a weird way, and you press up to do a pursuit (as stated in manual). An Impossible Dust is a method of hitting the guy somewhat after a dust, and getting your ass back down. During this state, the opponent cannot recover, and it opens new opportunities for the combos.
D, pursuit, D, D, 236K, 2HS, air combo and reset.
D, TKed Spin Kick pursuit, land, S, air combo
Other characters who do not have such an ability to get them back on the ground, like Sol, would have to do a guard method. When you press two buttons together, you get the green thing around you. When you hit D, you do a slight pursuit then press the two buttons to activate the perfect guard. You hit the opponent with something, and then land. This acts like an Impossible Dust.
D, pursuit with perfect defense, S, land, DP HS, sj K, S, D
D, pursuit with perfect defense, D, land, 2HS, Dust loop (must be near wall).
You do not have to hold the perfect guard for more than a second, so don’t worry about taking off too much tension.
About the 2D to Bandit Revolver (1-hit) RC, Dust loop, no there is no way to do that without using tension. Either use it, or lose it. Besides, what else are you gonna spend it on?