1. You will proabably be able to find a taxi willing to do it but do expect them to charge you insane amounts. Same for most bookable transportation you usually find online. Even Uber is expensive since they only offer Black car service right now.
I would find a private driver and negotiate with him for a reasonable price. The trip is 80 km + 80km return (slightly less if you take a paid highway) so 20 - 40 euro for gas. I would expect to pay around 150 euro.
2. Most museums in florence are open on Sundays and close Mondays.
4. Most people would reccomend doing Pisa as a half day trip by train from Florence. The trip by train takes about 1 hour.
5. Academia museum, Michelangelo square, Dumo square and cathedral, Signoria square, Venchi chocolate gelato is the short list