Is the destiny of non-Muslims who performed good deeds Hell, and what is the evidence for that from the Quran and Sunnah?

Yes, for whoever doubts this is one of them. The proof for this is Allah’s saying: (And whoever desires other than Islam as a religion – never will it be accepted from him, and he, in the Hereafter, will be among the losers) [Aal 'Imran: 85]. And His saying: (And whoever disbelieves in him among the [various] factions – then the Fire is his promised abode) [Hud: 17]. And His saying: (Indeed, those who disbelieve in Allah and His messengers and wish to discriminate between Allah and His messengers and say, "We believe in some and disbelieve in others," and wish to adopt a way in between – those are the disbelievers, truly. And We have prepared for the disbelievers a humiliating punishment) [An-Nisa: 150-151]. In Sahih (definition) Muslim, the Prophet, peace and blessings be upon him, said: "By Him in Whose Hand is my soul, no Jew or Christian of this nation hears of me and then does not believe in me, but he will enter Hellfire." The Ummah has reached a consensus on this.