I notice when looking in settler inventory that they usually have 5 to 10 rounds of ammo for their default weapon. My question is, if I give the setter a better weapon of a different caliber, how much ammo do I need to give them, and do they replace it themselves or do I need to go around to them and replace ammo after an attack?

You only need to give settlers one round of the appropriate ammo for the weapon you want them to use. After that they can fire indefinitely. This also works for followers, but only if they've been sent to a settlement and are not currently accompanying you.