Is it true that all foods coming from animal sources are forbidden?
No.
Milk, eggs, and fish are authorized to be eaten on days of abstinence. Again, according to the Missal published by the Society, the traditional days of abstinence are All Fridays of the year, Ash Wednesday, Saturdays during Lent and the Ember Days during Lent. All other days of Lent are days of partial abstinence (that is, meat may be consumed at one meal only), Ember Days outside Lent, and the vigils of certain feasts.
By the way, the regulations on fasting and abstinence have changed often during the life of the Church. The Missal from which I obtained this information says that the regulations have, at times, become more strict and, at times, become less strict. The regulations I have listed are those that were in effect immediately prior to the start of Vatican II.