Sorry to hear of your suspension. That's right don't go ghost or circumvent your suspension in anyway. ebay is well known in being able to trace your current and/or new details so in the end you will be in deeper trouble.
Did ebay give you their reason for your suspension? And from your end was it reasonable?
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You can generate invoices are from PayPal once payment is made and confirmed, so if you accept PayPal payments it doesn't matter where you sell you should be able to provide your customers with an electronic invoice.
If you open your own SaleHoo Stores, you can also generate your own invoices.
Hope this helps!