> Would they be higher with easier access to firearms?
Quite possibly. Is there a reason to think they would not?
And yes, culture where suicide can be honorable or beautiful ending will likely have more suicides. Western tradition was treating suicide as a sin and stigma.
Yes, It could be dishonorable to use a firearm.
A little bit of pain may make you look more manly, such stuff.
The socio-cultural embedding of an an act that makes it logical and rational.