Flex; you mentioned that you aren't comfortable giving them advice because you aren't the child's parent... BUT you ARE the secondary caregiver, who spends close to, if not AS MUCH, time with that child. In my mind that makes you equally capable to assist in the raising and development of their child.
Now, do I think you should go in, guns blazing, and tell them they are doing it all wrong?? No, as much as it would probably feel good to do so, lol! But there are ways to correct parent behaviour as much as there are to correct children's behaviour!! Just like you did with the "flopping".....
I would absolutely put my foot down about payment. Do you charge it in advance?
And about the Fridays; I think I would let that one go, as it sounds like it was pretty open ended between you. Of course, common decency dictates that they should have let you know, grrrrr.