two simple plumbing questions

Search YouTube for sprayer diverter valve replacement...there'll be quite a few videos to pick from. Your shut off valves likely have buildup (from mineral deposits, corrosion, etc) in them. As Scott said, turn the main off...up to you if you want to replace the shut-offs or just leave your water off long enough to replace the diverter. Get the diverter out and take it with you to the hardware store so you can get the right replacement...if they don't have one you may get to put it all back together until you can get one off the internet, or just buy a new faucet.