(Note that a “Yes” answer may mean “in some cases”, not necessarily “all cases”.)
1. Traditionally, has the Church ever permitted, in any cases whatsoever, a person to receive Communion, when the person is known by his pastor to be guilty of committing an objectively grave sin on a continuing basis, without first repenting and confessing that sin?
Yes. This occurs sometimes in the confessional, when the confessor realizes the penitent is committing a grave sin, which the penitent does not know is gravely immoral. Sometimes the Church advises the confessor to leave the person in ignorance, yet they can still receive Communion.
So the claim that the divorced and remarried, who are committing objective mortal sin, but not actual mortal sin, cannot receive Communion, is false. It is within the authority of the Church to give or deny them Communion.
2. Traditionally, has the Church ever permitted, in any cases whatsoever, a person to marry when the spouse of a previous valid marriage, which has not been annulled, is still alive?
Yes. If the first valid marriage is a natural marriage to an unbaptized person.
3. Traditionally, has the Church ever permitted, in any cases whatsoever, a person who is aware that he has committed an actual mortal sin, but who has repented (as far as he is able to judge) with perfect contrition, to receive Communion prior to a good Confession?
Yes. The Council of Trent permitted this for priests who need to say Mass and cannot get to another priest for Confession.
4. Has the Church ever, prior to the Pontificate of Pope Francis, permitted married priests and married deacons to be exempted from the practice of perfect and perpetual continence (so as to have marital relations)?
Yes. Currently, married priests and deacons are not required to refrain from marital relations — despite claims to the contrary by conservative commentators.
5. If a Catholic Christian has a valid ratified, but not consummated Sacrament of holy matrimony, is there any act either spouse may take, of their own volition, to dissolve that marriage?
Yes. If the spouse takes vows in religious order, their non-consummated marriage is thereby dissolved (not annulled).
Ronald L. Conte Jr.
the reproach of Christ 
Yes of course, all those things can happen and are permitted at least sometimes! The accusers look for accusations, not for logic. And frankly, their own “tradition” starts much later than the first centuries practice. I just entered in Churchmilitant and was scared to death. Those people will accuse their own mothers and send them to hell, if somehow their mothers do not support their outright fanatical views that belong to the dark ages, not to the early Christianity.
Isn’t it said also that Satan will actually try to accuse the soul based on her own failures, without the mercy of God being involved? I think St Faustina has something like that. And someone wrote of the antichrist, that he will be “righteous” man who will look for the faults of every individual to control him, and if disobeying to accuse him and punish him through his own human faults. Thanks God we are not in that time yet! Thanks God that cardinals Sarah, Muller, Burke do not have the chance to sit on the false prophet’s throne and restart the Inquisition burning of people! If there is a precursor of the antichrist in history, that’s it.
Perhaps we need Vatican III after all those synods to decide those questions once and for all. As Vatican II did. If needed new dogmas, let they be made, at the discretion of the Holy Father.
How about Jesus and John, that obvious intimate spiritual relation of our Lord even though without the shadow of sin. The Church should clarify what it means in practical terms for the faithful and how they could imitate that obvious example of greatest love Jesus left to us. He wouldn’t show it if it shouldn’t be followed. No, it is not only the celibate life of western priesthood. It is the spiritual intimacy that John also had with his disciple. Other saints had it too. Why for example the friendships in the youth are systematically destroyed by priests if someone wants to follow vocation? Because Jesus didn’t have it? Yes He had it. It is a time to look back to what Jesus did Himself in His Divine wisdom, and not what the Church did in her darkest pages of history.
I wonder if we should afford the same compassion to the papal critics as Amoris Laetitia afforded the divorced and remarried. I think it’s very important that Ron cries out in the wilderness, but I know where the papal critics are coming from, and I did not know I was wrong.
The papal critics have accused the Pope of heresy and apostasy, have accused the Church of being infiltrated by Satan at the highest levels, have made themselves judges over every Pope and Council, over doctrine and discipline. They also treat the Roman Pontiff and all those in communion with him with the greatest malice and contempt (which is a mortal sin). They are leading souls away from Christ. Also, the claim that Satan has infiltrated the Church at the level of Popes and the Magisterium is blasphemy against the Holy Spirit. So…what would Christ say?
{7:19} Every tree which does not produce good fruit shall be cut down and cast into the fire.
{7:20} Therefore, by their fruits you will know them.
{7:21} Not all who say to me, ‘Lord, Lord,’ will enter into the kingdom of heaven. But whoever does the will of my Father, who is in heaven, the same shall enter into the kingdom of heaven.
{7:22} Many will say to me in that day, ‘Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and perform many powerful deeds in your name?’
{7:23} And then will I disclose to them: ‘I have never known you. Depart from me, you workers of iniquity.’
{7:24} Therefore, everyone who hears these words of mine and does them shall be compared to a wise man, who built his house upon the rock.