Hullin 114: Mother's Milk

How literal is the Torah's phrasing of "mother's milk"? Does it really mean the milk of the mother of the given animal, or all milk? Clearly, all milk - and the Gemara provides the logic for that as well as a verse to teach it too. But why both? Also, how do we know that it is prohibited to consume meat and milk that have been cooked together? The product of that which is prohibited (the cooking) is considered abominable, which would prohibit eating that product. Plus, Rambam's inference that there was once an idolatry where the worship was done via cooking milk and meat together, which was determined to be true, centuries later.