broken valve

Not a plumber and really have no experience with this sort of thing. I help maintain my Aunt's "winter home" in Texas. We had a freeze a month back and it appears there was some freeze damage to the master bath. A valve burst, I got that hastily patched and everything critical resolved. But it...

I'm trying to shut off the sink so I can fix the leaky faucet.... but these valves on this particular sink are different than all the others in my house. Picture 1 looks like you'd turn it 90 and it would shut off, however it just spins in circle. So I thought maybe it was a push pull but as you...