(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.