
No.
Yes.
I don't know what you mean by "speak out," but a woman is forbidden in Scripture to be an Elder/Bishop/Overseer/Pastor over men, teaching them in this role. Women may teach each other and even provide co-ed training, say, in evangelism, or apologetics, or perhaps speak to an entire congregation about what it is to be a missionary in Botswana, but taking a position of spiritual leadership and instruction over men is not biblical.
If they are engaging in homosexual behaviour and are professing to be a born-again believer,
1 Corinthians 5 indicates very clearly that such a person is to be ejected from the congregation to which they belong. If, though, a non-believing person struggling to be free of a homosexual impulse comes to church looking for help in Christ, they ought not to be turned away, but told the truth of the Gospel and invited to know and walk with their holy Maker.
No. "The proof of the pudding is in the eating" hold true here, I think. Don't proclaim to me that you're a healer, show me you are. And do so in the manner of the biblical record, not in the modern ridiculous and false style of "healing" that is typical of the Word of Faith and New Apostolic Reformation "movements."
No, only God has this prerogative. We ought to obey Him rather than men.
Yes, sort of. There's no point, though, in putting a man over you as an Elder if you intend not to believe a word he says. Check out what he tells you, of course. But the Bible commands believers to accord Elders special respect as Elders and to appoint them as Elders because they have proven themselves to be godly and well able to teach. This wouldn't be a man whose every word you suspect is a lie.