Whose duty is it exclusively to consecrate the Holy Eucharist?
It is the duty of the priest exclusively, who has been validly ordained according to the rite of the Catholic Church (LXXXII. 1).
Is it also the priest's duty to dispense this sacrament?
Yes. But a deacon has the power to dispense the precious blood in a chalice on those occasions when the Church permits communion under both species; he is also able in case of need and in extraordinary circumstances to dispense communion under the species of bread (LXXXII. 3).
Can a priest who is in the state of mortal sin consecrate and dispense this sacrament?
He can do so validly, but he sins gravely in doing so (LXXXII. 5).
Has the Mass of a bad priest the same value as that of a good priest?
The value of the Mass is absolutely the same in either case in so far as it is of the sacrament of Christ's Passion. But as regards the prayers said during the Mass, those of the good priest have an efficacy such as those of the bad priest have not. But all these prayers have the same efficacy on the part of the Church in whose name they are said (LXXXII. 6).
Next - The Catechism of the Summa - Tertia Pars - XXXV. OF THE MINISTER OF THE SACRAMENT OF THE HOLY EUCHARIST (B)