Paris Museum Pass and Lourve

1. Yes, if you have a reservation and ticket/pass, you may use any open entry.

2. It depends on how busy it is. September/October is still high season in Paris, and particularly this year with the Rugby World Cup in town until the end of October.

3. Reservations not required for the Orangerie.

Note that you need to book the Louvre as early as you know your dates as they have limited tickets for Museum Pass holders and you may find it 'sold out' while others are merrily buying tickets on the web site.

The Carousel entrance when we were there this spring was limited to those who had tickets or memberships -- so yes, you do not need to enter at the Pyramid. You will probably be okay late; no guarantee but since the ticket is not 'read' by a machine until you get to a wing, it should not really matter. The guard at the entrance to the carousel security line will probably not look that closely at the time -- of course always a risk of an officious official.

Yes, if you have a reservation and ticket/pass, you may use any open
entry

I'm not so sure. The Paris Museum Pass website states this:
https://www.parismuseumpass.fr/t-en/sites-a-paris/musÉe-du-louvre

"To book a time slot: log on to ticketlouvre.fr, select "Visitors with a Paris Museum Pass", choose the day and time of your visit, and indicate your name and your PMP number (The OP evidently has already done this). You can then download a QR code that will get you through the first checkpoint at the entrance to the Pyramide du Louvre (the only way to get in). You will then need to show your PMP at the various checkpoints in the museum, located under the Pyramid."

So, the entry point may be different for visitors using the pass.

If we miss our time (traveling with a preschooler so that is always a
possibility) is there still a chance we could show up (assuming the
line isn’t crazy long). We plan on going on a Thursday in late
September, so I don’t think this is high season.

Scott, personally I wouldn't push your luck: do everything you can to show up at the reserved time. As Tocard said, September/October is still very much high season so expect Paris to be busy, and staff at the entry are under no obligation to bend the rules. Let's just say that these tickets are in enough demand that I wouldn't take the chance of being turned away at the door because I missed the appointed time?

Orangerie requires a booking. In the first week of Sept, all slots were taken.