Delicious Pasta restaurant in Florence and Authentic Gelato?

Everyone will have an opinion but for me the best gelato is Vivoli.

Hints on finding good gelato.
1) artisanal, fatto in Casa means "handmade, gourmet"
2) berry flavors are great. Some great gourmet flavors. Can't go wrong!
3). Should be a "dull" subdued color. Bright colors that "pop" are generally the result of coloring added.
4). Metal pans
5) "flat" profile. Gelato that is fluffed up with fruit bits on top is basically "store bought" quality. True gelato has a consistency that does not allow for it to be "fluffed/stacked" up. Should look flat in the pans.
Too many flavors - not enough time!

We just try to have gelato twice a day ... Or more. Ask at hotel for their favorites. I have never met a gelato i didn't like

We've been known to have, on more than one occasion, Peroni beer and gelato for dinner.....

Another vote for Vivoli!

I fell in love with mango gelato in Italy!

Re: reservations for restaurants, it depends. It doesn't hurt to have one for a restaurant that is recommended in guidebooks. Most places you can stop by in the morning or afternoon and make a reservation for the evening, or ask your hotel desk staff to make a reservation.

I've eaten Trattoria Bordino's inexpensive daily lunch special about €10, via stracciatella 9 near Ponte Vecchio, across the Arno river from the main sights.
The lunch special I had was the Bistecca alla Fiorentina (similar to a T-bone) with a salad. The steak was cooked at high heat for only 3-5 minutes a side, nearly charred on the outside but the interior very rare and only warm, which is how that steak is traditionally prepared.
The pasta was actually very good, and the best part of the meal; but was not part of the special and is extra.
Check TripAdvisor reviews.

Best two gelato I was recommended by a local and to whom I fully agree:

Carabe- near Accademia. No bright colors or, fancy signs, very simple and you'll taste the fruit
LaCarraia- Just across the Ponte alla Carraia, modern and popular, flavors are on point

Delicious pasta....you're in Florence while pasta is a national staple, you're not going to find restaurants that exclusively specialize in pasta. All will have pasta on their menu, clearly some do it better than others. Make sure you're ordering pasta dishes that are more near regional rather than Roman or, S.Italian.

Reservations are highly recommended. Italian restaurants like to know who's coming and be prepared. If you just drop in, it's viewed as being inconsiderate and you'll be stuck near the door or, kitchen. Plenty of places will take drop-ins but, its best to make reservations either the day or, two before.