Paris questions for a newbie

There are brasseries which are open all day and serve food, even at 6:30 PM.
There is Hippopotamus - sort of TGIF Fridays - which might be good for finger food or a substantial dinner.
I would not expect anything to be open on Easter Sunday or Monday for that matter.
You could always "leche la vitrine" in the chocolate shops, or if you're early enough, go to a supermarket and get some chocolates. Get there before noon.

I can attest to the fact that the Rue Mouffetard market is open on Easter Sunday morning because we did it last year. There were people dancing and celebrating at one end of it and it was delightful. We bought lovely things for a picnic and then went to the Jardin du Luxemburg and sat for a few hours enjoying our food and wine, and watching the children playing with sailboats. The park has a lot of activities for kids and would be a great place to spend the better part of the day, weather permitting. If you want to do same, perhaps you could do Versailles in the afternoon, as you're only planning a partial day anyway.

...my partner and her 11 year-old daughter. This is my first time going on an international trip with a child...

Just a "heads up". If your partner is divorced from the child's father, I believe (though I might be wrong) there are some legal hoops that have to be jumped through before the child can be taken out of the country. I'm not sure what they are as I've never been in that situation. But people do it all the time so they must not be insurmountable. Perhaps someone who has been in such a situation can give you specific information.

This museum, Muséum National d'Histoire Naturelle, looks pretty good for family fun.

From "Timeout" - "At the Natural History Museum's Grande Galerie de l'Evolution, stuffed creatures parade majestically through their various habitats. Animals of all kinds teach children about the diversity of nature and, in the endangered and vanished section (where a dodo takes pride of place), about the importance of protecting them.

Also in the Jardin des Plantes complex are the small Ménagerie zoo, separate pavilions containing hunks of meteorites and crystals in the Galerie de Minéralogie et de Géologie, and the bony remains of fish, birds, monkeys, dinosaurs and humans in the Galerie de Paléontologie et d'Anatomie Comparée."

For Question 1, if I were doing this I'd make sure everyone ate something around 5:30 or 6 pm - at least a sandwich. And I"d bring a snack, something like apples or granola bars, Or maybe have a late lunch but that wouldn't carry me through - I'd be snarling hungry by 20:30. Your results may differ, just my two cents.

It is not easy to find a place with a kitchen still open at 11:30 at night. I would probably plan to eat before hand or inquire if the tour includes a stop for food or a picnic. It would be odd to schedule something that long at that time without some sort of food stop built in. At any rate make sure you have lined up an 11:30 dinner ahead of time and make sure you have sandwiches or something before embarking on the tour unless it clearly includes a dinner stop.