Yes, photos have been allowed in both (no flash, selfie sticks or tripods) since mid 2014.
You need to enter the museum at the time you collect your tickets. From Uffizi.org (not the official website but has some good info):
"Can I visit the museum at a different hour or on a different day than the one written on my voucher?
The simple answer is NO, you cannot. The museum handles visitor flows by selling a specific number of tickets for each date and time. So you can only visit the museum on the date and time written on your voucher."
B-ticket (official site) also states that "Once payment has been made and the transaction concluded, it is no longer possible to change or cancel a booking." That pretty much implies that once you commit to a slot, you can't just come at another time or ask to do so.