1-Rav Sheshes Mishoum Rabi Elozor Ben Azaria said first that he can answer for the world to the Heaven Court on all matters because the world is like intoxicated after the destruction of the Bais Hamikdosh. 2-Then he qualified his statement that he can answer for the entire world "Midin Tefilah" only. 3-Then Rabi Chanina added that "That's for being intoxicated until the drunkness of Lot, but from the drunkness of Lot then the world can be Potur from everything"
1- On the first statement of Rav Sheshesh. How could he answer on a judge who is intoxicated while judging. The gemara explicitly stated that an intoxicated person cannot judge?
2-On the qualified statement "Midin Fefilah", the gemara said explicitly that the tefilah of a drunken person is "To-eiva" ?
3- On Rabi Chanina who said that if drunk like Lot everyone is Patur from everything, yet why did he not exclude tefila and judging ?
(1) You are correct. Certainly his claim of defense cannot exempt the world from every type of judgment. The Gemara could have asked such questions, but it preferred to ask from the Beraisa which states clearly that an intoxicated person "is considered a Pikei'ach with regard to every matter." The Gemara answers that Rav Sheshes' original intention was to say that he can exempt one from the Din of Tefilah alone.
(2) This refers to one who has the option of Davening at a later time when the effects of the wine have weakened, and yet he did not wait and he went ahead and Davened under the influence. Such a person's Tefilah is considered a To'ei'vah.
One who will never be able to Daven with a sober mind, though, who does not know whether he will ever become sober again, such as one who is "drunk" with the adversities of Galus, his Tefilah is certainly not a To'ei'vah (for he has no other choice). (That is, drunkenness is all relative to the person's "normal" state. A person that fundamentally lacks in concentration must Daven as best he can, and is not called drunk even if he acts more drunk than a drunkard!)
(3) The words of Rebbi Chanina are not referring back to Rav Sheshes' statement. Rather, Rebbi Chanina is referring to the Beraisa which said that one who is intoxicated is like a Pikei'ach. On this Rebbi Chanina said that if the person has reached such the state of intoxication of Lot, then he is considered like a Shoteh, and not a Pikei'ach, with regard all matters.