When sprayer is used, all water to sink (faucet and sprayer) shuts off, how to fix?
Your sprayer unit is not designed to sit at full system pressure, so the faucet unit that it came with is specially designed to shunt water towards the sprayer hose and head only when the sprayer lever is pressed. The faucet itself has an integral diverter valve to perform this function, it sounds like yours is not working right.

All faucet brands use their own proprietary diverter mechanism, you will need to get a manual for your faucet to get it apart and replace the valve. It might look something like this: