talos furious charge and hammer of wrath/ slam

I started playing with a pain engine. Good stuff.
How does hammer of wrath and slam work together? The special rule says no AP2 included with hammer of wrath, that I get. But can I double my strength for it?

Furious charge adds +1 to strength till the end of the phase the special rule says. Is that just for the charge or does it last till the end of the round or till the enemy is slain? It seems to me that it means the end of the round.

HoW states that you need to use the profile strength. Only Baron Sathypants have been FAQ around this.

The FC, is during your assault. His next turn you dont have +1S. So its only for the charge.