"Moons the size of Earth, orbiting a gas giant, are clearly a possibility. I see no real problem with two Earth-sized planets orbiting each other. the problem I would encounter is proximity of the local Sun for warming, and other radiation requirements. If orbiting a gas giant, there would be a monthly eclipse that could chill the moon to sub-zero temperatures."

What the difference between an eclipse and the daily rotation of earth? If it actually was a month duration orbit, than your eclipse would be probably be about same length of time as one of our nites (or less). But there are many factors involved. First the Gas gaint will be giving off heat and visible light- Jupiter does and we are probably talking about a bigger Gas gaint, and also a warmer gas gaint becauses it closer to the Sun. The coldest time on the planet would be on the farside at nite. If the orbital period was one month then you would have a long night on farside.
The orbital periods of Juptier's major moons:
Io Orbital period (days) 1.769138
Europa Orbital period (days) 3.551181
Ganymede Orbital period (days) 7.154553
Callisto Orbital period (days) 16.68902
[More massive gaints will have faster orbits- and being closer to star will require orbits to be fairly close to gas gaint {unless they are strange orbits}]
Finally why would chilling moon to sub-zero temperatures be a problem, we have places on Earth which spend a considerable amount of time at sub-zero temperatures, and Earth has gone through eras of time where most of the planet spend most of the time in sub-zero temperatures [not including all the volume of the ocean though- at at least not much below freezing]

"Also, would the moon be tidally locked, and, if not, are there other Earth-sized moons in the vicinity of this giant? If so, they would be tidally affecting the proposed "Earthlike" moon in ways that would likely make the moon uninhabitable -- for us, that is."

The moons will probably be tidally lock. Don't understand why other moons would make it uninhabitable.

"Complicated, to say the least."

Agreed. Offering lots of possible variations- some might allow intelligent life to evolve

"Can life exist on such a world? I believe so, but we would be hard-put to live there with any real comfort."

Well same could be said for living any other place other than southern california:)