The white cloaks are an independent military force. They come from a country called Amador. They are kind of a cross between the KKK and the Nazis. People are afraid of them so they go pretty much anywhere they want to go except for Tar Valon. But they seem to always have a contingent outside of Tar Valon hoping to catch an Aes Sedai or a warder alone. The Aes Sedai are unable to use the power as a weapon except against dark friends or in the last defense of themselves or warders.
I can see why you would think that about the warders without knowing the back story. The warder bond is a weave of the one power. It confers certain things to the warder like faster healing, the ability to go without sleep, the ability to sense creatures of the dark one if they are near, etc. They also feel what their Aes Sedai feels including pain and vice versa. When a warder's Aes Sedai dies they go mad and usually get killed in battle because they just go berserk. Many just ride off and die. If a warder dies, his Aes Sedai goes through terrible, debilitating grief for a time and is unable to touch the one power because she can't find the calm needed. Warders know this before they agree to be bonded.
Reds don't take warders, the other Ajahs usually take one, the greens, who are the battle Ajah, take multiple warders and often marry them. When their Aes Sedai are in the tower they train together and help to train young men who come to the tower hoping to be a warder.