First, he didn't even wonder if Quirrel wasn't possessed/imperiused by Voldemort, even after the Hogwarts security system identified the killer of Hermione to be Quirrel ?

There was a healthy portion of HPMoR's readerbase that wasn't convinced that Quirrell was Voldemort, and unlike the readers, Dumbledore hasn't read canon. I don't really think you can take this as evidence for Dumbledore's stupidity.

Second, he actually voice that he was stupid, what does he gain in doing so ?

Nothing, but from his perspective, it's not like he would lose anything, either, and he was frustrated. People often vent aloud when frustrated.

Third, how could he think he can defeat Voldemort with the "frozen time" spell when Voldemort is aware of that spell ? Voldemort has a horcrux network, he can just kill himself. The only hope would have been to use the "frozen time" by surprise.

I imagine the Mirror would have trapped his soul in it if he had killed himself, or prevent the Horcrux network from coming into play by other means; else Quirrell would definitely have thought of it, and likely so would have Dumbledore.

And finally, he faces Voldemort without even bringing Fawkes with him ? Whyyyy ? If he had Fawkes, he would largely have had the time to teleport Harry to safety while Harry was saying his heroic "I was stupid don't save me".

According to Quirrell, the process cannot be stopped after being set in motion, and this probably also applies to removing people from the process (at least without exotic artifacts like the True Cloak of Invisibility). It's uncertain, then, whether bringing Fawkes would have accomplished anything, and on top of that, we don't actually know where Fawkes is; it's very possible that he's off somewhere else accomplishing some vitally important task Dumbledore set for him.