Is it possible to have a multiple same item auction with a BIN option for each item/purchase? I thought you can list in eBay more than one of the same item with a staring price and a buy it now price, but once a bid is placed the BIN goes away. What am I doing wrong? If I try to list multi same items in Auctiva with a BIN, I get errors saying either the Lot count or Number of items count is invalid?

You can sell multiple items in an auction (Dutch auction) or with a fixed price (Buy It Now) but not both. See these links:
Multiple Items
Fixed Price