The push button piece that goes in the window frame

Thanks for posting! The hardware you are searching for is referred to as a vent latch. Yours appears to be exactly identical to the 26-362 Sash Vent Latch. To determine if this is the correct replacement for your repairs, carefully look over the dimensions and compare them to your existing latch.

Alternate image for 26-362

Alternate view of 26-362