Great questions!
In the Lutheran Church, we recognise 2 Sacraments; Baptism and the Eucharist. However, we also sometimes talk about a third Sacrament, Holy Absolution. This is still retained in the Lutheran Church, as the Office of the Keys, the power to forgive or retain sins, belongs to the whole Christian Church. This is why we confess our sins in our services, and if anyone is burdened by sins, they are free to confess them privately to their Pastor, and the Pastor will absolve them and comfort them with the Gospel.
We rightly reject the notion of Purgatory. It's not found in the Bible, nor in the Early Church. It's a late development born out of a series of errors, and it's counter to the Gospel, for, in Christ, all our sins are paid for in full. We do not, nor cannot, pay for our own sins. Not even in part. So, needless to say, Mass for the dead - Prayers and sacrifice made for people to shorten their time in Purgatory - is very problematic. It's a bit of a long walk to explain how Purgatory developed, but it comes out of a wrong understanding of Sin and Justification.
It's not common, but some Lutherans use a kind of rosary, only it doesn't include any prayers to Mary or saints. It's simply used as a tool or reminder to be diligent in prayer. I don't use it myself, but I can recognise it as an adiaphoron - something neither commanded nor forbidden by Scriptures.
The reason why the Roman Catholic Church retain these doctrines and practices has to do with where we get our authority from. Perhaps it's helpful with a simple comparison:
Authority in the Roman Catholic Church: The Roman Catholic Church, which includes Scriptures, Tradition, and the Pope. Given the succession of the Papal office, their Tradition is somewhat progressive (in contrast to Eastern Orthodox who also holds to Scriptures and Tradition, but which ended with the Ecumenical Councils in 787. So their Tradition is somewhat fixed).
Authority in the Lutheran Church: Scriptures alone. Though we still value Church history and tradition.