I have a feeling you are not using the New Ajax Based Squeeze page form
How to Make a Squeeze Page Using the WordPress eStore Plugin
Please use this one as I am dumping the old one (it still exists for backwards compatibility). Going forward I will only enhance the Ajax based one as it’s cooler and causes less problem.
The AWeber integration works exactly the same way like selling an individual product so you should be able to specify a listname that will be used just for this product.
As for the stock control for free downloads… free download kind of implies free/unlimited so I didn’t do the stock control part here but I do understand your scenerio. I should be able to implement the stock control option for free download very easily so I will add it for you.