The main difference between the Closed Hip Twist and the Open Hip Twist is the starting position. The actual "hip twist" part is the 4-1 count where the lady does the swivel/twist. For an Open Hip Twist you begin in an open facing position with one hand hold (man's LH to lady's RH) and do almost exactly what you described. A Closed Hip Twist is similar, but you start from a closed dance position, normal hold. It begins with a Natural Opening Out Movement with the lady doing the hip twist action on the 4-1 as before.
I'm not as familiar with the Turkish Towel as other figures, but I'll see if I can help. First, I think this is only a syllabus step in Cha Cha, not in Rumba. You could do it in Rumba I guess, too, but it would be considered an open level figure then. So I'll talk in cha cha timing instead of rumba timing. I'm not sure I understand your description of the figure (e.g. whose head is the hand going over?). It looks to me like you're taking 4 measures to complete the lady's underarm turn and get into the position for the Turkish Towel. It should only take 2 measures -- RH to RH hold, do a forward half basic leading the lady into an Alemana style turn (234&1) and over the next measure you lead the lady (who is walking forward) behind you and towards your left side, ending facing the same way you are and taking her LH in your LH (234&1). That's the position for the main part of the figure. Now you do the "towel" style action that gives the figure its name -- it's supposed to look like the man is using that lady like a towel to dry his back.
I'm not sure what the "in" and "out" terms are supposed to mean, but by their position in the step description I'd guess they refer to the towel style action. With the lady on the man's LS the left arms are slightly lowered and the right arms slightly raised to make a comfortable position. Then the man steps back OP, lady forward OP on 2, they replace weight on 3, then cha cha cha to the side for 4&1. Now the lady is on the man's RS and the arm positions have switched so the right arms are slightly lowered and the left arms slightly raised. The man steps back OP, lady forward OP on 2, they replace weight on 3, and cha cha cha to the side again to end with the lady once again on the man's LS, arms positioned as the first time (4&1).
I'm a little unsure of the ending, but it starts as before, switching sides 234&1 but on the 1 count the lady is lead a bit more forward and into a spiral turn. I think your "spin girl anti-clockwise" on the next to last 41 is this spiral turn. The final 234&1 is supposed to be like a back half basic for the man (but with the chasse going forward) and the second half of the Spiral for the lady. I think this basically means she's got some more turn to make and she's going to keep going in a generally forward direction which is why the man's chasse has to go forward to follow her. This last measure is danced solo with the couple regaining hold at the end in an open facing position.
I hope this description is helpful. It's often hard to describe moves in words, but we try. If you can get someone to demonstrate it for you or help lead you through it though, that should help even more.
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James Marshall
marshall@astro.umd.edu
http://www.astro.umd.edu/~marshall