Well, Jesus said that the Father will not judge, but the Son will be in charge of judgment on the last day, so they're sort of acting separately there.
We say that they have different roles. So, while the father might not "judge", he would decree that the son judge, or something like that. The Holy Spirit would have a role in there too.
A way of thinking about the 'trinity' is this.
It's an egg. Where some people describe the 'trinity' as Water (which is seperate in states and therefore a bad analogy), the egg is a better image.
When you purchase eggs at the supermarket, you don't buy egg whites or egg yolks or the shells seperately, they are purchased as one.
In other words; the Father, the Son and the Holy Spirit are all parts of an egg. Hope it helps.
(Idea from a sermon preached by the Pastor at my church)
Everything I have been able to figure out says that the sin was specific to Jesus' ministry on earth in that they were saying Jesus' power came from Satan. Since Jesus isn't ministering directly anymore, we can't even commit this sin if we tried.
I don't really worry as a Calvinist, because I trust God to be fully in control of salvation anyway, so its not like you lose out on salvation because you made a stupid mistake.