Combat values can't be modified or replaced.
0 Points

So for powers like Quake and Energy Explosion. How does this interact? Same with Charge and Running Shot? Same with Blades. Do you just use printed values or can these not be performed? I remember Outsiders was similarly worded but that was a long time ago.

QUAKE When this character makes a close attack, they may target all adjacent opposing
characters. If they do, they gain KNOCKBACK (for this attack) and deal each hit character 2 damage instead of normal damage.

ENERGY EXPLOSION RANGE: Make a range attack and all other characters
adjacent to an original target also become targets. Hit characters are dealt 2 damage

BLADES/CLAWS/FANGS When this character makes a close attack against a
single target and hits, you may roll a d6. If you do, deal damage equal to the result instead of normal damage. Minimum result is this character’s printed damage value -1.

Damage delt is not a combat value. Hierophant doesn't;t interact with those powers.

CHARGE POWER: Halve speed. Move, then CLOSE as FREE -or- make a close attack.
RUNNING SHOT POWER: Halve speed. Move, then RANGE as FREE -or- make a range attack.

Charge and Running shot will move at full speed.

Edit:
PULSE WAVE RANGE: Halve range, . Other characters within range can’t
use powers or abilities (for this action). Make a range attack targeting all other characters within range and line of fire, including at least one opposing character, using printed defense values for each targeted character. Each hit character is dealt 1 damage instead of normal damage.

In addition, PW will Half its range.

All correct except for what you say about Pulse Wave. The concept is the same for Charge and Running Shot. Pulse Wave WILL NOT halve its range, Range is a Combat Value.

We played it the opposite....since RS and Charge require a replacement value to move and attack, you couldnt use them. Im not sure you can simply ignore half a power. In this game, cant beats can.

See my signature

AHAHAH, my sight is so bad that i saw a DON'T before "half its range".

The "Halve speed" it's not a requirement, it's the 1st of the 2 effects of both powers (the second effect is "move and make a range/close attack or a RANGE/CLOSE action as free).

I dont know about that. If you dont halve speed youre not really CHARGING. Many powers outright say, CHARGE, but do not halve speed. IE, do the power, this is different, then do the rest.

They dont say CHARGE, ignoring replacement values and modifiers.

Honestly, I can see it go either way and its going to be all of one or the other. This just makes more sense to me.

Sorry for not answering to you before, now back to the topic.
What you see written in a power's effect explanation is an effect. When you read that you don't have to halve you speed is because you can avoid to apply that effect or part of the effect, or effects, written in it. If it was a requirement it would have been written in this way: "Halve speed. Move and then, if you halved the speed, make a CLOSE or close attack."
Charge doesn't say anything about replacement values or modifiers, those things are in the Rulebook.
The Tarot in question doesn't specify what effects are affected by it, to know what is affected and what doesn't we need to know what is a replacement and when there is one or not.
And NO, it can't go either way: it is a replacement or it isn't, you can apply the effect of the Tarot or you can't.

Additionally, if full move charge were written that way, you couldn't perplex up your move to charge further, or perplex up your attack to hit better, nor could you use blades in the attack, not to mention several other replacement values or modifiers that could be applied.