Not that I'm looking at ever running this figure given her combat values, but if I do (I'm looking at running some Justice League teams in the near future), I'd love to know just how she works nowadays.

MYSTICAL WARDS: Amethyst ignores the Mystics team ability. When a character is given an action to activate a power and attacks Amethyst, she can use Shape Change.

How does the final line of Mystical Wards interact with the following powers, if it even does? In short, the question at the heart of this is the timing of when players declare the use of certain powers.

BLADES/CLAWS/FANGS: When this character hits and would deal normal damage during a CLOSE action, you may roll a d6.

QUESTION 1: I'm assuming that Blades/Claws/Fangs gets around Mystical Wards, as the choice to roll the d6 for Blades appears to be made after the CLOSE action has long been declared? It reads like "Make the choice for a CLOSE, but tack on the d6 later when you want to use it."

PRECISION STRIKE: When this character attacks a single character, damage taken from the attack can’t be reduced below 1 and the target decreases its d6 roll for Super Senses by -1.

STEAL ENERGY: When this character hits with a close attack, after resolutions heal 1 click if one or more opposing characters were damaged by that attack.

HYPERSONIC SPEED: Move, then make an attack, then move up to ‘your speed value minus the number of squares just moved’.

QUESTION 2: Similarly, what about Precision Strike or Steal Energy? The one triggers on attacking, and the other on hitting with a close attack, but attacks can be made without them being their own actions, such as during Hypersonic Speed, which is its own POWER action. What happens here?

Thanks for your time and consideration.

I believe you are over-thinking this. Regarding HSS, this same question would apply to every power granting an attack, Charge, RS, CE, RCE, EE, various special powers, etc. The bottom line is, did it take an Action of some type(even FREE) to grant an attack, and that the attack occurs within the action, then she can use Shape Change. If the attack occurs outside of an action, such as many 'after actions resolve' effect, or some the ways that some characters can make an attack without using an action, then she can't use Shape Change. Whether the attacking character can use BCF, PS, or SE is dependent on that character's powers, as there may be special circumstances, but the use, or lack of use, of these in and of themselves have no interaction on her ability to use Shape Change.

HSS will trigger it as you are giving an action to make it happen.
Steal energy, BCF and Precision Strike would not for the reasons you mentioned.

The only thing that matter for Amethyst's trigger is if the attack is the result of being given an action specifically to activate a power. Blades, PS, Steal Energy, are all triggered effects, you do not give actions to activate them.