Anyone in the supply chain is a potential party to products liability lawsuits, not just the supplier and retailer. So you have manufacturers, shippers, etc...
It is indisputable Amazon is in the supply chain of these products, and of course of a case by case basis their role(s) for each product is different, including, but not limited to: at minimum promoting the products on their online marketplace, facilitating the purchase of the products (potentially conducting the transaction itself via Amazon gift cards), storing/warehousing product, shipping/delivering product, in some instances they are the wholesaler of product, etc...
They should be thankful for the time they had escaping obvious legal liability and the opportunity to get a decade+ head start on any new marketplace that wants to compete and will have to contend with these legal risks. Amazon will fight it to tooth and nail to the end, and then start with appeals, they could spend billions a year and lose but it would be worthwhile because the simple number of dangerous products on their marketplace some of them resulting in death.
So I would imagine that yes, you could.
Strange question, in USA, the is fact you can sue anyone for anything in a civil suit. It's up to a court to decide whether your case has merit or not.
I once worked on a case where the client was hit by a bus operated by the County (so a local government in a particular state), the suit was not entirely barred but there was a cap on damages which would not otherwise exist if say it were a bus being operated by a private company (which would of course generally have a commercial insurance policy as well). It has been almost 10 years but at the time I think the cap was $200,000. Interestingly there is/was a mechanism to request the state (I think the state legislature) waive the damages cap on a case by case basis, but unless your firm was politically connected and donated to political campaigns good luck with that.