It's a little vague, so I'm not going to try and tell you what a strict
RAW interpretation is. But, it is almost always interpreted as so:
1) They loose 1 attack for that assault phase. Meaning: It doesn't last forever. They end up being at -1A for as long as their engaged with the
DA and it never goes higher than -1. Once they break free of the
DA, they regain that attack.
2) The minimum 1 is a per model after bonuses are applied. So, if a model with 1 base attack and has a bonus for 2
CCW, strikes with only 1 attack.
And, I am someone who says don't buy the power and keep
DA out of
CC!