Sellers will sometimes opt to remain in the house after closing via a short-term rental agreement. As the new owner, be sure the purchase contract and rental agreement stipulates that the sellers repair any damage they cause after the closing date.
Earnest money is money put down to demonstrate your seriousness about buying a home. It must be substantial enough to demonstrate good faith and is usually between 1-5% of the purchase price (though the amount can vary with local customs and conditions). If your offer is accepted, the earnest money becomes part of your down payment or closing costs. If the offer is rejected, your money is returned to you. If you back out of a deal, you must forfeit the entire amount.