You might want to visit the nocturnal Dali exhibition in the Parc de la Villette (until 21 January). I went and thought it was outstanding.

That looks amazing! Thank you!

yes you can. Maybe it would be better to start with market and take the train for "Versailles Rive Droite" from St Lazare rather than the train for "rive gauche/château". You can save few steps walking to the market from rive droite to the market and then to the château. And you will like it at the end of the day! If you want to check the gardens and the Trianons, you could walk a lot (or rent a golf cart or ride the road train).
no need to go on a weekend for the fountains as they don't operate in winter. But check the market days (Sunday is one of them but I think there are other days).

Don't forget about the Luxembourg Gardens and the Pantheon. The Rodin Museum is a personal favorite museum and very close to Invalides.

Sacre Couer and Montmarte

When you're in the Latin Quarter for your pottery store appointment, think about grabbing food and sitting and enjoying a picnic in the luxembourg gardens, one of the most peaceful and relaxing gardens in Paris. You could also take as troll down Rue Mouffetard past place de la contrescarpe, a quintessentially charming Parisian plaza - Rue Mouffetard is adorable and has lots of fun boutiques and shops. It culminates in a market street at the end. Au P'tit Grec is my favorite crepe shop on that street - enormous crepes to go.

You may want to take into account sunrise/sunset in Paris in December when planning any outdoor activities'. You're looking at sunset at 4:55 p.m. most days, which will come quickly after time inside a museum. If you are mixing indoor and outdoor, I'd look at the extra opening hours for museums. Some are open late on certain days - the Louvre open until 9:45 on Fridays, which will allow you time outside/parks and then take advantage of the late hours for the museum.