Hey Jody. Thanks for all the thorough information! This is a 15-180 Pivot Shoe, which uses Series 190 Coil Balances. Stamps of 4 and 5 would indicate you need the S190-440 4 pound spring and S190-540 5 pound spring, respectively. However, that would equal 9 pounds of support on one side of the sash. Since the coil springs on both sides of the sash should be identical, that would mean you'd have 18 pounds of support total. You cite the sash weight at 13 pounds. Please double-check this if you haven't, since 18 pounds of support would be much too strong for that sash weight--you'd basically have trouble keeping the window closed!
Did you ever have that issue, before the coils broke? If so, it's possible you had too much support to begin with. Otherwise, please double-check if the weight is in fact 13 pounds. Let us know if it is, and we'll tell you what coils to order instead.
As to your other question, it is probably best to replace the coils on both sides at the same time. Coil balance systems technically are modular, meaning you only have to replace what is broken. So for instance, if your old housing is OK, you don't need a new support clip (15-181) or bushings (15-182). But balance springs tend to wear out faster when paired with older ones, so with the springs themselves, it's best to replace everything at once.
Let me know if that all makes sense, or if you have any other questions.