1. If im not mistaken they were well-rested.
2.
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Read the bottom right panel of this page, Naruto said he wanted to punch Sasuke until his eyes opened, key word: wanted. Which means he acknowledged he couldn't because he couldn't move.
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"You still want to fight in your condition?"
Sasuke was not talking about Naruto's inability to move, he was talking about how badly damaged Naruto was. The first panel showed Naruto saying how he can't attack because he still cant move, so obviously Sasuke was not talking the inability to move.
"Of course, I'll never give up!"
Naruto already acknowledged he couldn't move which means he couldn't and was unable to fight, the conversation is obviously not pointing towards the current condition in which they were both unable to move, they were talking about the injuries they suffered from the battle.
So obviously he meant after they were able to move to continue the fight, and Sasuke admitted defeat.
Like i also said before, in a fight, when a fighter admits defeat, that automatically makes the other fighter the champion.