Which window. Alan e series to purchase?

Thanks for your photos. Based on what I see here, you have either our S351-30 or S390-30 S351-31 or S390-31, depending on the depth of the bottom shoe. That's the only difference between them. I recommend measuring your shoe and referring to our dimensions to confirm the best match.

Comparison of the S351 and S390 balance shoes.

I'm sorry for the confusion; in my initial response, I suggested the 30" long balances, but that was a typo on my part. I meant to suggest the 31", which conforms with the given stamp. Sorry about that! In your case, S390-31 sounds like the best choice.

The options are required, yes. Those indicate the strength of the spring, which is possibly the most important detail when it comes to picking a replacement balance. If the spring isn't calibrated properly then your balance will not be able to do its job. 

In your case, you will probably want to keep using the old stamp of 3040. Two balances with this option can carry sashes weighing 23 through 28 pounds.

Lastly, regarding your window being hard to operate, that does sound like the result of bad balances. When these parts get old, the springs lose their tension or sometimes even corrode. As a result, they can no longer properly regulate the operation of the sash and it becomes much harder to open and close. New balances will usually fix the issue.

Yes, if the larger window is 32 pounds then I absolutely recommend bumping the stamp up to the 3050. Sometimes the original window installers miscalculate this sort of thing. It's unfortunate but it does happen. The sash weight doesn't lie, though, so I always defer to that.

In my experience sun exposure isn't that much of an issue for balances, since they're almost always covered by the track and sash. Sun damage is a very real risk for the top sash guides though, which are the plastic retainers at the top corner of the sash that keep the balance in place. More often than not the direct sunlight will cause those guides to go brittle, which leads the balance to breaking through them and shooting to the top of the track. That's the only instance I can think of where balances are negatively affected by sun exposure, though.