For example, I go and buy something for $100, and auction that something starting the bidding at $1, and then hope for the best. Almost sounds like a gamble. Which is why I am asking if auctions are permitted according to Islamic law?
While buying something for $100 and auctioning it at a starting bid of $1 is a highly questionable business practice (why not just start the bidding at $100?), there's no reason to believe it's forbidden Islamically. Even the prophet himself is reported to have auctioned off items.
Auctioning is merely a method of determining the final price for a sale; so long as this final price is decided fairly and agreed upon by both parties when the transaction itself takes place, it's just a sale like any other.