Mostly it'll be flintlock pistols, rifles, muskets, and blunderbass, in order to give power to non-benders. The heroes will all be gunhaters naturally.
Possible. There was gunpowder in the original series, as well as some prototypical cannons in the third season. Guns would be a natural development from those.
Who says they should hate guns? Benders may not use guns because they don't NEED guns! I always kind of liked to picture a hard-core Sokka with a shotgun (of the blunderbuss variety.) Maybe the normals of this season will pack heat!
They could hate guns because of corrupt militias that use guns to massacre civilians or benders. Arrows, swords, and other such weaponry (and bending too) require training and discipline, and thus much time and money to create armies with. Mass-produced guns mean instant armies of whoever happens to be on hand. Anti-bender revolts could get bloody.
That's a silly generalization. You mass distribute guns — especially older, primitive guns — without any training or discipline and you end up blowing yourself up. Just because guns are not as flashy as non-firearm weaponry doesn't mean there's no training or discipline involved. By that logic they should also hate spears or javelins since they are also easily mass produced, required relatively less training compared to swords, and far outranged swords. And, you forget that corrupt militias have already been using bending and other non-firearms to oppress people (remember that episode with Zuko defending the town) for far longer. Lastly, guns = instant armies may be true now because of modern industry and guns like the Kalashnikov, but any guns likely to be developed in this time will be like the older arquebuses. Not to mention the need to manufacture gunpowder and ammo. And given that any gun industry would be in its infancy given that there wasn't one before, they're still at least years away from any sort of large-scale mass production, much less "instant armies".
Gun might have existed in the Gaang's time. The tech we see during the Gaang's time implies they had to have had the possibility of such weapons. They might have just not been that pronounced for various reasons. Namely like those stated above, the guns of Gaang's time were too unstable for mass use and the high bender count in armies would look down on such weaponry. The Anti-Bender mentality mixed with more advanced and stabler weapons could very well allow for the anti-bender forces to take up guns or refine gun related tech into guns to equalize the common man against the "magical" benders.
Although there is argument for both sides, I doubt it. Having guns would continue the creator's habit of introducing nuanced, mature subjects. It would also be consistent with the probable theme of technological advancement. Lastly, it is a good way to even the odds between benders and common non-benders, although low-level earthbenders would obviously have it easier than low-level airbenders. That said, guns would be more difficult to pull off. American cartoons are bound to certain expectations, far more so than Japanese ones. I seriously doubt we'd see anyone killed or crippled onscreen by gunfire. Because of that, it would be very easy for the gun-wielding bad guys to degenerate into Imperial Stormtrooper Marksmanship Academy, which would make them nonthreatening. As much as I would like to see it, I don't think the creators would risk that when, in the original, there were several threatening nonbenders, although admittedly they were in the top three percent.
One thing you have to remember is the style of gun that they would have had are very very very inaccurate. They were really only effective with massed soldiers and very short distances. It really wasn't until the late 1700's that very accurate guns cam, even then it took trained marksmen to be accurate over a dozen yards.