Museum passes, etc. ahead of time?

The free Tate is there because of admission to the special exhibits that may or may not interest you. The main museum needs no ticket nor pass.

Paris (5 days): Will do the museum pass. Sounds like this is bought on
arrival?

Yes, purchase the Paris Museum Pass (not the overpriced Paris Pass) when you get to the city. Just don't plan to buy it at the attractions with the longest queues, like the Louvre. Use the tabs on this page to see where all of the outlets are:

http://en.parismuseumpass.com/rub-t-points-of-sale-3.htm

Versailles (covered in museum pass, but what about the fountain
tours/passes?)

Tours and musical water shows are not covered under the pass. You would need to purchase additional tickets for those.

http://en.parismuseumpass.com/musee-chateaux-de-versailles-et-de-trianon-64.htm

Notre Dame, Louvre, Orsay, Saint-Chappelle (all covered).

Notre Dame itself is free; the pass covers the Towers and the crypt. The pass doesn't allow priority access to the Towers. At Sainte-Chapelle, the pass doesn't allow priority entry through the security line, only bypassing of the ticket line.

Is the opera house worth a visit -- or perhaps with cheap tickets to a
performance?

Palais Garnier isn't covered under the Museum Pass. We did it as we skipped Versailles, and self-toured it on our own but guided tours are also available. Visitors are only allowed to access public parts of the building, and the auditorium may be closed for rehearsals, as it was when we first arrived. "Cheap" is a relative term for performance tickets but I see some recital/small ensemble prices from 15 € and up: search Palais Garnier under venues (2nd link below) not Opéra Bastille.

https://www.operadeparis.fr/en/visits/palais-garnier

https://www.operadeparis.fr/en/ticketing

Florence (3 days): Firenze pass. Also sounds like better bought there,
but I'm unsure. Should I also get a reserved time for Uffizi?

Yes, buy it there. No need to make a reservation at the Uffizi if you have the pass: that allows you priority entry although there could be a short wait if the museum is filled to capacity. Read the the FAQs on the website for other questions you may have:

http://www.firenzecard.it/?lang=en

I bought accademia tickets ahead of time. We were able to be in FIRST.... great photo w David got to see other exhibitions before it got packed,which it did.

We also got tickets online for the tower at pisa. They only let in 20 people at a time, and slots do sell out. I did the bapistry, beautiful, probably never sells out.

The Accademia is covered under the Firenze Card so no need to advance tickets or reservations if using it.

Once we got a pass as a present from one couple that enjoyed their last evening in Paris but hasn't used the pass. Who knows, maybe it won't be so interesting running from one exhibition to another just because you have a pass.

For Paris, the Museum Pass is for 2, 4, or 6 days. Since you have five days, get a 4 day pass, and do the Eiffel Tower and other non-covered sights on the day you don't have pass coverage. Yes, buy it there, at a tourist office or at any non-biggie museum (i.e., not the Louvre or Musée D'Orsay).

The advance tickets for the Eiffel Tower may be sold out for your dates, but you can get in line early in the morning or can take the stairs (which have a much shorter line than the elevator). Or you can see it from the viewing point at the Trocadero (free) or the top of the Arc de Triomphe (covered by your pass). These views are great by day and by night; since I had the pass, I actually climbed the stairs in the Arc de Triomphe twice, and was glad I did.

The Firenze Pass is now VERY expensive (€72!); are you sure you are doing enough covered things to make it worthwhile? Or, would you do better just with advance tickets for the Uffizi and the Accademia?