Do you have one set of weapons for everyone or does each character have their own set? If it's the former, does selecting a weapon stop other characters from using it?
Does this also apply to weapon mods?
Weapons and also weapon mods are available for everyone once you find them. So once you find a certain weapon, Shepard and everyone in the squad can use them at the same time.
You can use different mods on a weapon for each squad mate, but every mod is available for everyone once you find it or buy it.