Even if you were at 0.5% BAC (legal driving limit is 0.08%, and 0.5% would kill a lot of people), that's still about the alcohol percentage in NA beer. Unlikely to have any effect.
If you drank the same amount of 0% ABV water in that time, you’d probably die of water intoxication, so I’m not sure any adverse effects of the alcohol would be noticeable.
Point is it could be a lot of alcohol for the mosquito.
No, the alcohol wouldn't. Unless you distilled all that beer and ingested the alcohol alone. The massive liquid intake would kill you though.
The liver doesn't store alcohol, so how many grams you ingest in total doesn't matter, only in what concentration. Keep in mind that alcohol is perfectly soluble in water too.
(~10 pints of blood in the donor, 1/10 of a lot of alcohol...)