If she is working full time for you, I would be very attracted to a $3,000 monthly retainer if I were her.
Definitely you can kindly request (AKA demand since it's your child) that they use a different photo without your child.
Community pool! Museum! Park! Movies!
Discuss this ahead of time with your employer! Find out what they expect of you when it comes to holidays as far ahead of time as possible so you can manage your own expectations.
I don't think so! I think experience is one of the greatest teachers when it comes to children. If you were to get one, I think becoming CPR certified would be a great choice!
For that, I would charge upwards of $35-$50 an hour. You are functioning in multiple roles at once and you have very high expectations placed on you, so you deserve to be compensated as the professional you are functioning as.
Some 5-month-olds might enjoy a dance party (5-month-old version of course) where you hold them and bounce along to some sweet music. In psychological studies, this has been shown to increase a baby's liking of you as they move at the same pace and rhythm as you!
If you are able and willing, go for it! However, if you are looking for a firm work schedule, don't be afraid to say no or make it clear that in the future, you can't work more hours than you agreed upon.