1. If a person is unknowingly in mortal sin, and takes the Eucharist, what are the dangers? Should those in such a state simply be excused for being ignorant of the gravity of their state?
In order for a sin to be a mortal sin, one of the conditions is the person must be willfully aware that it is a sin and commit it anyway. For example, "You shall not commit adultery" is one of the Ten Commandments. For a Christian person to engage in an adulterous relationship it is a mortal sin for every Christian knows the Ten Commandments, and to participate in such a relationship is clearly contrary to God's Law and an utter rejection of His Authority in one's life. They choose self pleasure and lust over God. No Christian could possibly NOT be aware of this sin as it is foundational to the Judeo-Christian faith. In short, one cannot be in mortal sin without KNOWING they are in mortal sin and in need of reconciliation.
2. Where does the Roman Church outline these dangers?
The Catholic Church teaches this in the Catechism of the Catholic Church (I can post references if you wish) and straight from Scripture (ditto on references).
3. Should a priest be concerned about the possibility of giving someone the Eucharist who should not have it? If so why? If not why?
Yes, a priest should be concerned and if he KNOWS the person approaching him for Eucharist is in mortal sin, he should refuse that person. If the priest has no knowledge of the person's state, then he should not refuse the Eucharist and if one is receiving is not "receiving worthily" then this is between that person and God, and that person eats and drinks judgment upon him/herself.
I hope this helps.