Not a very high risk of that happening, unless you're doing shady stuff involving lots of money.
Well since some states don't even require filing of list of directors for multi-party LLCs, and all you have to provide is a contact name and address (for which you can list your as your agent with thousands of other businesses listing the same address and agent) if you do it right there's no way they can link you.
1. It's not illegal to give false information to eBay, it's illegal to give false information without consent of the person whose information you're giving to eBay, or trying to use false information to commit fraud.
2. As I said above, you can keep information of who owns the LLCs anonymous.
Unless you have millions in stake here, why sue eBay? Just create more accounts and sell more. Remember, eBay WANTS you to sell more, as long as you're not doing anything shady. There's a reason why eBay is not way way way more strict on shutting down stealth accounts even though it's technologically possible for them to do so. Stay under the radar and don't sell fakes and generally follow eBay policies and it's not that difficult to get up and running again.