If Temple of Sinnoh is in play, can I use Archeops' "Primal Turbo" Ability to attach a Rapid Strike Energy from my deck to a non-Rapid Strike Pokemon?
Yes, you can use Primal Turbo to attach Rapid Strike Energy to a non-Rapid Strike Pokemon. Normally Rapid Strike Energy would be discarded immediately, but Temple of Sinnoh removes all effects of Special Energy attached to Pokemon, so Rapid Strike Energy would not be discarded. But if Temple of Sinnoh's effect goes away, then Rapid Strike Energy would be discarded.
Source: TPCi Rules Team (2023-04-06)
Can I use Porygon-Z's "Crazy Code" Ability or Archeops' "Primal Turbo" Ability to attach Spiral Energy to a Pokemon that isn't a Rapid Strike Pokemon?
Yes you can, but then it would get discarded immediately. However, if that Pokemon was Paralyzed, Spiral Energy would remove the Special Condition.
Source: TPCi Rules Team (2021-07-01); TPCi Rules Team (2023-04-06)