When refering to the flaming and frost weapons giving both cold/fire damage as well as the radiant damage when used, it says nothing about if the At-Will of the weapon is used, just that the weapon is used.
In order to deal fire damage with a flaming weapon, you have to activate the at-will free action ability to convert it from weapon damage to fire damage. That is a power of the magic item.
"When you use a magic item as part of a racial power or a class power,
the keywords of the item’s power and the other power all apply."
So, when using the at-will free action to convert it to fire damage, you add the keyword (it does not supercede the existing ones), so you would be dealing 1/2 fire, 1/2 radiant.
You cannot just assume that the At-Will is used.
No, it actively has to be used. However, if it is not active, then it's keyword does not apply.
It doesn't say that. So it gains the cold/fire keyword to add to the radiant and then splits the damage between. If the At-Will had been active, then the damage would all be cold/fire as it states in the Frost/Flaming weapon entry. No At-Will weapon power was used though. The weapon was used, not the At-Will.
Okay, let me play this out. The example will be using a paladin with a flaming longsword, as in the DMG.
By your explanation...
- Weapon set to "weapon damage."
Melee basic attack - Deals 1[W] plus Str bonus (weapon damage).
Holy Strike - Deals 1[W] plus Str bonus (half fire, half radiant).
Valiant Strike - Deals 1[W] plus Str bonus (fire damage).
- Weapon set to "fire damage."
Melee basic attack - Deals 1[W] plus Str bonus (fire damage).
Holy Strike - Deals 1[W] plus Str bonus (fire damage).
Valiant Strike - Deals 1[W] plus Str bonus (fire damage).
By my explanation...
- Weapon set to "weapon damage."
Melee basic attack - Deals 1[W] plus Str bonus (weapon damage).
Holy Strike - Deals 1[W] plus Str bonus (radiant damage).
Valiant Strike - Deals 1[W] plus Str bonus (weapon damage).
- Weapon set to "fire damage."
Melee basic attack - Deals 1[W] plus Str bonus (fire damage).
Holy Strike - Deals 1[W] plus Str bonus (half fire, half radiant).
Valiant Strike - Deals 1[W] plus Str bonus (fire damage).
To me, the weapon damage and fire damage are interchangeable, but it does not negate the existence of other damage types due to powers, and the example in the PHB seems to support this.