First, not all Calvinists are double predestinarian. I believe it depends on when they think the decree of God was made.
Some, of course, believe that God did not have to predestine to hell if He only predestined the elect to heaven. That would make logical sense. If you don’t specifically appoint someone to heaven, then they are logically going to hell, but not because they were specifically appointed to it.
Any Christian prays, proclaims, follows because God has instructed it. We don’t know how it factors in. The Calvinist knows that his bible says the same as others: “there fervent prayer of a righteous man availeth much.”
Therefore, he prays. He doesn’t pretend to have such great insight into what God can and can’t do that he disregards God’s own instruction.
That's correct. There is an order of decrees and it depends on the timing of these decrees. At one time I tried to study this but it really gets into some very deep scriptures. I felt there was a danger of perhaps reading something into scripture that wasn't there. It's almost like eschatology. Some people are very firm in saying they understand it. I don't think anyone really does.
But branding every Reformer as believing in double predestination is wrong. Most great Reformers such as John McArthur, John Piper or even old time preachers and teachers such as Charles Spurgeon or Matthew Henry clearly don't.
That's kind of a given, and does not mean that God decided to send them to hell as in picking and choosing before time who He made for the purpose of destruction, never giving them a chance to repent as He has commanded all men to do.
It’s in their confessions. If they disagree with their confessions that’s one thing but if they agree with their confessions by definition they believe in double predestination. Fudge words aside.