Before I start: GO CAUTIOUS AND CONSERVATIVE WITH ALL OF THESE PROGRESSIONS. This is always important, but even more so when there are no pits available.
For back twisting:
Just train it half by half. Start with a strong back layout with the arms out to the side. Once the gymnast can do this comfortably, she should land, then drop one arm and turn in that direction. Eventually, she'll be able to drop an arm and turn before she lands. Once this is comfortable, the same approach can be applied to learn a 1/1, then a 3/2, then a 2/1. You only mentioned 1/1s and 2/1s, but I would STRONGLY reccomend you not neglect the 3/2 -- it's worth the same as a 2/1, it's easier for most gymnasts, and you can connect other skills out of it much more easily.
Front twisting:
Again, learn it 1/2 by 1/2. Start with a strong front pike and front layout. Then, have the gymnast do front pike, open, jump 1/2. Then pike-open-1/2 before landing. Once this is completely comfortable and consistent, progress to front 1/1s and 3/2s in the same manner.
Double backs:
Unless you have a strong and confident spotter available who has experience spotting double backs, don't even bother with this skill if you don't have a pit available; it's not worth the risk.
If you DO have such a spotter available, start with very high back tucks. Next, have the gymnast do a back tuck to her back onto the level 4 vault mat (and you can build this up further by piling more mats on top -- I recommend continuing this until the gymnast can confidently do a back tuck to her back on a mat stack which is at least shoulder-height to the gymnast (head height or higher would be better). She should be comfortable doing this without a spot.
Before moving on to actually flipping the double:
-Make sure the gymnast knows where she is in the back tuck to her back. She should be seeing the mat (without opening the tuck) after the first flip before rotating back to her back.
-It would be a good idea for the gymnast to learn a double back on the trampoline first. This is not absolutely necessary, but will certainly help the gymnast's confidence and aerial awareness.
I want to emphasize again: if you do not have 100% confidence in your ability to spot this skill, you shouldn't bother teaching it, because it simply isn't worth the risk.
Giants on bars:
I've seen hourlong seminars on this that still didn't cover even close to everything there is to be said on the subject. I'll have to give the abbreviated version here:
If you're training it without a trench bar or strap bar, the easiest and most effective way is probably the babygiant-freehip method.
Prerequisite skills:
-Excellent tap swings
-Strong baby giant
-Strong freehip
Once the gymnast has all three of these, she can simply combine the first half of the baby giant (swing toes and hips up over bar towards support) with the second half of the freehip (push out to swing without allowing hips to contact the bar).
Tsuks:
Like a double back, you should not train these without a pit unless you have available a coach who is comfortable spotting them. Also, double backs on trampoline will help the gymnast's awareness for this skill a lot.
Start by putting the level 4 vault mat behind the vault table, and have the gymnast practice a 1/2-on/roundoff to land on her back on the mats. The goal is for the gymnast to be able to do this without any pike in the hips or close in the shoulders -- she should be able to make it to her back without coming out of the hollow position at the end of the 1/2-on/roundoff.
Once she can do this, pile a few more mats on. The goal is for her to be able to make it to her back without breaking position with the mats stacked to table height or higher.
After this, there's nothing to it but to do it. Again, this should be done with a spotter who is able to effectively spot this skill in case anything goes wrong.
Always be cautious and conservative with multiple-rotating skills -- remember, the gymnast's life is on the line.
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