No you only need 2 pieces to survive in the crater of Death Mountain, and only 1 piece for the road before the bridge to Death Mountain.

Should I upgrade Flamebreaker armor?

To scale Death Mountain and survive Breath of the Wild's harshest heat, players need to buy and upgrade the full Flamebreaker Set. While the set can be purchased in Goron City for a hefty sum of Rupees (3,300 altogether), the Flamebreaker armor is downright essential for exploring Breath of the Wild's Eldin region.

Is there a set bonus for the Flamebreaker armor?

The Flamebreaker Armor, alongside the Flamebreaker Helm and Flamebreaker Boots, compose the Flamebreaker Set. When each piece of the Set has been enhanced at least two times by a Great Fairy and the full Set is worn, it provides a Fireproof Set Bonus.