As a Buyer it a standard for you to disclose your financial information. Doing so allows the Seller and his representative to make an informed decision on the strength of the Buyer. This especially helpful in a multiple offer scenario. The Seller would want to choose the strongest Buyer, most likely to complete the transaction and close on the expected settlement date.
Having your earnest money held by the Selling broker is standard. Allowing the Selling broker to hold is just as safe as using your choice of title company to do the same.
The amount you choose to use for your earnest deposit can be any of the 3 choices you listed, but the school of thought is the more money used for earnest the less likely the Buyer to change their mind after committing to the purchase. Remember should you change your mind after signing the contract to purchase, those earnest funds could be kept by the Seller, The Seller would have the right to claim liquidated damages per the standard contract.
If you were inclined to go with a smaller earnest amount your Buyer's Financial Information should reflect funds in excess and would back up your ability to purchase a home in this price range. Your pre-approval letter and BFI are both used to support your ability to purchase.
If you have any other questions feel free to ask.