Coil balance
Hello there. That assembly looks like it might either be the Series 210 or Series 161, depending on the thickness of the bottom coil shoe. See below. Measure your shoe's thickness to see which of these you need.
Now, a problem is you have that additional coil housing and spring on top. You can use the 15-086 Housing and the Series 180 Coil Balance springs for this. Basically the tandem housing just stacks on top of the bottom shoe like a totem pole.
Finally, for each replacement spring you have to choose a spring weight, which reflects the weight the springs support. The stamps on your old system suggest you need 19 pounds of support on both sides of the sash. To make things simple then, go with either the S161-10 or S210 10 pound shoe and spring, depending again on which series you need--and then the 15-086 shoe and S180-09 9 pound spring to stack on top. For the bracket, see the 16-030.
Since the Series 161 is 9/16" thick, you will want to go for the Series 161 Coil Balance assembly.
No, the 16-030 is sold separately.