sprayer

I want to install a sprayer with the toilet. In order to do that I need to shut off the water supply to the toilet. But my shut off valve is not working when I move it clockwise. How can I install it while shut off valve is still supplying water? I thought about using bucket or similar...

Hello, I'm looking to remove our kitchen house sprayer from it's feed, and place a brass flare cap over it. But what kind of connection is in this picture? It's hard to get to so I want to know just how to remove it once I'm ready. And does it look like I'd be able to place a cap on it? Thank you