@Cole Evans, 1. you can decide in your offer how much you are willing to in as the initial deposit. If the seller likes your offer but doesn't like the amount of the initial deposit in your offer, the seller can make a counteroffer with a higher initial deposit. Generally though, in California, your initial deposit will be 1-3% of the purchase price. To answer your question, yes, you must put in the full amount of the initial deposit into escrow.
2. You can make any contingencies on purchase that you want. So, for instance, you can have a contingency that the seller must provide you all of the Air BNB receipts for the past two years within 17 days of the opening of escrow or you have the right to cancel the transaction and get a full refund of your deposit from the seller. The escrow will request reimbursement of any out of pocket expenses and may have a small charge for their services, if you cancel.
3. Unfortunately, no, the realtors are not correct and do not understand California law. You cannot withdraw or cancel a transaction for any reason. You can only cancel the transaction for a good faith reason as provided in your purchase agreement.
4. Yes, you can request tax returns, in particular Schedule E, which should provide you the relevant information.