He fired once face to face with Kogoro. I think it was on the episode where Kogoro was asked by someone to be a model for painting. I do not remember the number of that episode exactly but it was around season 2-4. I dunno if it's a filler though.The second one, Im sure he remembers the events just at the time the needle hits him.
As for the third one, I'll agree but I doubt that he is that too lazy to even wonder about it. I'll just assume that he just doesn't mind it all since he takes the credit anyway.
Yeah that's a bit overboard. It's trying to create a reason to plug the holes in the plot. And anyway, Conan didn't ask for the creation of Stun Gun wrist watch if I remember. It was Agasa who completely thought of it and Conan had no say on the specifications of the watch. Plus the first time Kogoro was made to sleep, Conan didn't use the stun gun. Still, Kogoro acted the same like he didn't remember a thing.Also when Gin was hit by the Stun Gun? He did react to it, right? and he was able to stop its effect. That means the effect of the stun watch isn't immediate after hitting. So if there's a drug that delivers amnesia to the user, its effects should start just sometime after the needle hit the person, not when the needle hits the person. This means that the person should atleast remember the needle hitting him/her and everything before it.
Also, it seems like Kogoro sleeps continuously until at least Conan finishes his deduction. He never even waked up once, in the middle of the deduction. Unless he's faking it, this is kinda unrealistic lol.