Ciao Kathleen,
Lots of questions, let me start and go down and try to get them all!
Can I buy the uffizi annual pass before I get to the uffizi, or will I have to wait in line to buy it the first day?
The annual pass to the Uffizi (50 euro) will give you access whenever you want for a whole year and with priority entrance, so no waiting in line. You can buy it online
https://www.uffizi.it/biglietti - just choose the date from which you want it to be active. I would wait to get it maybe just the week before you come because the ticket is non-refundable, if your plans change you cannot request a refund.
Is there any pass like the firenze card that allows you to visit locations more than once?
Aside from the Firenze Card, which only includes one entrance per museum, there are other "friend of" passes for other museums that allow you to enter them multiple times.
There is one for the Accademia Gallery called the Friends of David - friendsofdavid.org/ - and there are annual passes for the Pitti Palace museums. Actually, if you want to visit the Pitti Palace museums, instead of getting annual combo passes for the Uffizi Gallery and the Pitti Palace, you could also do the Friends of the Uffizi card and get access to both complexes for 10 euros less -
http://www.amicidegliuffizi.it/diventa_socio.php?pg=8&ln=en
There is another for the Bargello - but at the moment not sure whether you can buy it yet as they are changing the NGOs status:
http://www.badcaos.com/themes/come-associarsi/
As far as skipping lines, yes it is a feature of the Firenze Card but this is only a main concern at the Uffizi and Accademia. Majority of other museums have much shorter lines.
Can you suggest a map that shows famous works of art in their locations in florence?
Not sure, there might be something you can buy more like a guide that has this information but off the top of my head cannot recommend one in particular. It's a great idea and maybe we can make something people can find on our site ;-)
Can I use an american debit card with a chip to buy bus tickets?
You can use your American debit card here ONLY if you go to your bank before you leave and make sure the PIN number and circuit is valid in Italy. Otherwise, plan to use credit cards like Mastercard and Visa or Amex.
Having said that, you most likely cannot use either to buy bus tickets, cash is always easier for the small purchases.
Can I use cash ( euros) to buy bus tickets?
Yes, best way to actually pay for bus tickets. Buy tickets BEFORE getting on buses at local bars and tabacco shops. While buses advertise they sell tickets on the bus, the drivers most of the time don't have them (or maybe don't want to take the time to sell them and people have then ridden the bus without a ticket, getting caught and fined).
Do you have to get your tickets stamped for the bus in an outside location before you get on the bus, like some train stations do?
Yes, in a way. The buses have a machine at the front near the entrance, so you stamp it when you get on the bus, not before.
Can you suggest a chain of drug stores or convenience stores that actually have storefronts in the touristy, congested downtown area near the ponte vecchio?
There are pharmacies (farmacia in italian) with a large green cross to identify them outside as such. You can find most medicines and off the counter items you might need there, including a few dry food items but not much other than that as far as food is concerned. You can definitely find toiletries there but not generally cheap or small, regular sized.
There is a farmacia on Lungarno degli Acciaiuli 5 just past Ponte Vecchio, another on Via Calzaiuoli, another on Via Condotta, all really close to Piazza della Signoria.
What are the options to get to and from the airport?
Take a taxi directly to your place so you don't have to worry about walking. There is a fixed set price from the airport to downtown hotels - this page has more info:
https://www.visitflorence.com/moving-around-florence/by-taxi.html
Is there a shuttle bus or train that goes as close to the Piazza Signoria as possible?
There are small buses in downtown. Bus C3 and D pass right behind Piazza della Signoria along the Arno river toward the train station. Bus C2 passes along Via della Condotta toward Piazza della Repubblica again toward the station and C1 and C2 in the opposite direction pass nearby. Download the bus map here:
http://www.ataf.net/en/timetables-and-routes/la-mappa-della-rete-atafeli-nea.aspx?idC=1123&LN=en-US
Do the museums allow you to sit on the benches?
Yes, if they are available, most do not provide them along the rooms through.
Is non-flash photography allowed in all museums?
Yes, you can take photos in most museum with no flash.
Is sketching allowed in all museums? Is sketching with a tiny watercolor palette (the kind that fits in the palm of your hand) allowed?
Sketching is allowed, watercolors are not. Again, there isn't much places to sit so not sure whether this is really doable for you if you can't stand for long. If you want to take along a portable chair and sit, I think you need to ask written permission ahead of time to each museum you want to do this at.
Can you bring a bottle of water into the museums?
Not allowed, unfortunately.
Can I bring a shoulder bag that has a pocket for my laptop computer into the museums?
Yes, you can take shoulder bags in. The important thing is to not hit artworks inadvertently with backpacks, so those are not allowed unless very small day packs.
Are there any musical performances at churches in Florence in september?
There might be but I don't know of any certain programs out for sure. If you check our events page for September toward the end of August, we should have updated it by then and added any interesting info we have found.
https://www.visitflorence.com/florence-events/september-in-florence.html
Hope this is helpful! Let me know if you have more questions we can help you with!