2) Men choose methods that are more likely to be effective; this is true everywhere, including places that don't have guns. This speaks to the same thing as my earlier comment: men choose methods that are end-directed, while women choose methods that communicate distress but are less likely to cause death.
I find it far more likely that they are just more concerned about leaving behind a messy corpse for someone to deal with/ are less willing to die painfully.
I prefer explanations that fit observed behaviour - men take larger overdoses, and neither a propensity
for violence nor a higher tolerance for messiness can explain that.
Likewise, I don't believe women become more violent or selfish as they reach middle age, yet they also start taking larger overdoses. It seems more likely there are specific problems that affect women at that point in their lives and/or they they feel less able to overcome problems they'd have coped with earlier (due to shrinking support networks, for example).
As for pain, I'd note that females are much more likely to self-harm than males (which, incidentally, is also messy).
Men kill themselves more even if you only look at intentional overdoses, which are about as non-violent as you can get. Older women also take larger overdoses than younger women - there are undeniable differences in intent between demographics.
Men are more likely to use guns, or in countries without guns, to use more drastic measures like hanging. They are less likely to discuss or telegraph their plans as well. No one knows it's going to happen, and they're more likely to succeed; "violent and aggressive" is a mischaracterization.
Women are more likely to attempt "cry for help" attempts like slitting wrists or popping pills, which are easier to intervene in. They are also more likely to reach out or discuss their plans for suicide, which makes the former (intervention) that much easier.