yes it's fine to shoot it all gunked up.
But it is a lot less accurate that way.
The barrel turns brown because it's bare brass and it will do that. it's fine.
Try to clean the paint off the gun very well each time you put it away. I recomend using warm water. most of the gun is brass, so nothing will really rust, but do dry it off well, ant don't put it in container wet, or what can rust will.