@Anna10179 First of all, I assume that the fact that there is a baby or children in the home was mentioned in the listing ad? When you book a home-share, you are subject to the lifestyle of the hosts. And if I were going to book a place long term, I would make sure to ask some questions first about things that were important to me, like privacy, quiet hours, potential for noise.
Babies cry, laugh, sometimes scream. That said, hosts should try to be respectful of guests just as guests should be respecful of the hosts.
In a home-share situation, communication is really important. No one is a mind reader, so the host may not be aware at all that her hanging out and playing with the baby in the living room late at night is disturbing your sleep.
So let her know in a polite way, and maybe she can hang out with the baby in another part of the house after 10 PM if that's when you go to sleep. Also, you can be pro-active for yourself, and use earplugs when you go to sleep.
As far as them using the bathroom that is meant to be for you, but you being expected to clean it, are they cleaning things you use, like the kitchen and living room? I mean things like vacuuming, floor washing, etc, not washing your dishes. If so, it doesn't seem unfair to ask you to keep one bathroom clean, unless you find they make a big mess in there.
That is also something to discuss with the host, if you feel you are doing more than your share. As you say, they don't charge a cleaning fee, so chipping in with the housework in a shared home situation is reasonable.
But if that bathroom was advertised as private, they really shouldn't be using it unless in an emergency situation.