About Slayers not using guns...
The Slayers don't live very long. They need to learn as many different ways of fighting as possible as quickly as possible. Hand weapons don't have to be reloaded. They can be repaired or improvised on the go. They can hack up demons, break into buildings, nonfatally incapacitate humans, and destroy vampires. They rely on the Slayer's own strength and are like an extension of her body. She'll never worry about an axe jamming or finding ammo for a stake. Also, Slayer powers do seem to give a boost to accuracy (see Buffy's skill with crossbows and knives) but it won't measure up to their advanced skill with hand weapons. Slayers almost always fight in pitch black. They often fight in closed-in catacombs, caves or lairs where big, scary monsters will be lunging at them from out of nowhere. Accuracy frequently decreases when something gets close to you, especially if it's a hideous creature from out of your worst nightmares, while using hand weapons becomes instinctual after training with them for long enough. Hand-to-hand edged weapons are easy to modify for mystical weaknesses of individual monsters--you can tip them with materials like silver or poisons. Guns are noisy, hard to take care of, take too long to become proficient for, and will get you in more trouble with the law and cause more collateral damage (Exhibit A: Tara).
With that said, it might be beneficial to teach some of the Slayers how to use guns. With hundreds of Slayers, they don't need to pack as much training as they can into one area. They can afford to specialize and focus more on individual training. A few could train with really advanced weapons in case they have another Judge moment, they could specify in different monsters, they could get a team of snipers or stealth operatives or magic-users. I got the impression from extrapolation and these issues that this is happening naturally, that the Slayers-in-training are gravitating to the subjects that interest them and they'll get more specialized on their own.
