Persecutions
Persecuting Roman Emperors (this is not a Catholic site, but it seems accurate)The Empire and the Early Church, a Tale of Persecution and Justice. An essay by Christopher Check, president of Catholic Answers.
Heresies
The Great Heresies from Catholic Answers
This entry from the Catholic Encyclopedia is quite long and isn't the easiest to read, but if you scroll down, you'll find a list of the principal schisms in the Church.
Recommended Reading
Kenneth Whitehead: One, Holy, Catholic, and Apostolic