S380 or S385 ?

Thanks for posting! It does look like you have either the Series 380 with a 1" shoe or the Series 385 with a 1-3/32" shoe. To determine which series is needed for your window, look over the dimensions from the diagram below to confirm the depth of your bottom shoe. Let me know if it does not match either measurement.

You'll also need to confirm the length of the metal channel; only the metal.

Comparison of the S380 and S385 balance shoes.

Once you've confirmed the series and the length, you'll need to determine the stamp option needed for your balance. Start by checking the metal channel for any stamps or markings. If there are none, you'll need to obtain the exact weight of the sash. There is a chart below the product description for each individual length that lists the weight ranges each stamp can support.

The issue you are describing with the window, is likely due to a missing or broken top sash guide. These are what guide the balance in the window channel and prevent them from shooting out of the window. Take a look at the video below for an idea on how to replace them. I'll need to see a photo of them to identify the correct replacement for them.

Yes, you are correct. The 2950 would be the correct stamp for your balances.

In regard to the plastic part you are referring to, this is the top sash guide. As explained, These are what guide the balance in the window channel and prevent them from shooting out of the window. 

Yours reminds me of the 18-178 Channel Balance Guide Pair. Take a look over the dimensions and compare them to your existing guides to determine if this is the right fit.

Alternate view of 18-178

Alternate image for 18-178