I learned move 2, 4, 5 and variants of move 1, 3 from a trainer and dance teacher. My translation will come from or be inspired by her version. She is rather senior. So some of the moves have been known and practiced in China for decades, where I expect the terminology to be more stable and uniform. As well, in China, a unique-ish form of body training called 形体 emerged over the recent decades, where people use moves adapted from basic dancing training/college for general exercise. Those moves tend to have uniform terminology. In other cases, moves that became popular later should have more diverse terminology.
仰卧 means lying facing up. 撑 means push up or pushing up.
I can't remember if there is a standard name for such a move. There might be a different standard name for having your two arms in a flat position.
拱桥腿 is used by some. 拱桥 means rainbow bridge. I prefer descriptive naming myself -- not metaphoric. My preference is a bit "German-like" (and arguably wider Chinese preference too).
四肢 - the four limbs
向上 - towards up (if you are into language, this is a rare case of preposition conjugated into verb)
四肢向上 for short also works. Since you can't do this move in any other way.
- You need to disambiguate.
If you mean lying flat, kicking one leg up while fixing the other leg on the floor, (head should be on the floor, arms are relaxed) then
Memory is vague on this one. But this version conveys the point.
仰卧 - lying facing up
踢腿 - kicks
前踢腿 - front kicks
So this combo differentiates from the possible sick kicks. It is inferred that you do not kick with both legs, because it is not productive to do so. (Raising both legs slowly is called 仰卧抬腿. 抬 means lift. The both part is inferred because it makes no sense to lift one leg.)
If you mean raising both legs, raising one more while losing one and alternate, (head area should be raised, but legs should not be near 90 degree up,) then
交叉 means cross
Obviously, be careful to not hurt the neck.
- Various possibilities:
The search links themselves offer more possibilities.
- Various possibilities:
Notably, 侧卧旁踢 seems to not work even though it should be fairly unambiguous.
躺地 means lying on the floor
躺 means lying (down)
踢旁腿 means kicking towards the side
侧 means side
侧卧, 侧躺 means lying on your side (at which point kicking to the side is the only sensible thing to to)
踢腿 means kick
抬腿 means lifting leg
So, if you mean kick, then don't say 抬腿; if you mean lift, use 抬腿 or 举腿 (not used in this case)
In specific context, I expect 侧板撑 or 侧板支撑 or 斜板支撑 to be legitimate since 平板支撑 has been accepted for plank. However, none of them yields the correct search result.
Meanwhile, 侧卧撑 is immediately comprehensible because 俯卧撑 means push-up.