QThe Oshi skill "Heeeyyyyy" of hBP02-005〈Murasaki Shion〉 was used once while 〈Murasaki Shion〉 with hBP02-087〈Murasaki Shion's Magic Wand〉 attached is in the center position, before it was moved to the back position due to baton pass.
Can I use the Oshi skill "Heeeyyyyy" once more?

ANo, you cannot.
If the 〈Murasaki Shion〉 with hBP02-087〈Murasaki Shion's Magic Wand〉 is moved to the center position again due to some effect, you can use it again.

QThe Oshi skill "Heeeyyyyy" of hBP02-005〈Murasaki Shion〉 was used twice while 〈Murasaki Shion〉 with hBP02-087〈Murasaki Shion's Magic Wand〉 attached is in the center position.
〈Murasaki Shion〉 was then moved from the center position, and moved back to the center position.
As Oshi skill "Heeeyyyyy゛" became [1/Turn] before becoming [2/Turn] again, can it be used once more?

ANo, it cannot be used.
As it is an ability that changes [1/Turn] to [2/Turn], even if the center holomem leaves the center position before becoming the center holomem again, there is no change to the number of times the ability was used that turn.