Need to replace this part

Sure, that looks like a coil balance assembly. It's comprised of our 15-180 shoe, 15-181 clip, 15-182 bushing, and Series 190 coil spring.

Unfortunately, they do not. Most of our coil balance components, including the products mentioned here, are sold separately and must be assembled by the customer during installation.

The rule of thumb is to take the weight of the sash and divide that by how many springs support it. In your case, that would be 4.

35 divided by 4 comes to 8.75 pounds per spring. The Series 190 doesn't come in that weight option, though. You could round up to the 9 pound S190-940 but I think you should get an exact weight, just to be safe. You had said that 35 pounds is approximate, but a more precise weight may make your decision a little easier.

I'm not sure what you mean, exactly. Are you referring to the screw that connects the spring to the pivot shoe? If so, there isn't really a trick to it. Both coils use the same hole and the bands should be flat enough to screw in without issue.

Your old stamp indicates a strength rating of 7 pounds, which would match our S190-740, That carries the same amount of weight

If your sash is 34 pounds, and considering you have 4 springs total, I would recommend using one S190-840 and one S190-940 per side. That's 8 and 9 pounds of support, respectively, so having them on both sides gives you 34 pounds exactly.

It can be a little tricky to stretch the spring out, but the method you described is exactly how it's done.