Typically, buyers will increase the earnest money as various contingencies have been satisfied or expired. Never make the earnest money payable to the seller. Don't gunk up your offer. In a hot seller's market, sellers are more likely to reject an offer that contains too many contingencies, or asks for too much. Asking to have the lawn equipment included in the purchase price may or may not be reasonable, depending on the price you're paying for the property.
Timing is everything.
While price is certainly important, other issues may be equally critical to a home seller. For some home sellers, when they close may be more important than netting a few extra dollars for the sale. Be sensitive to the seller's need for flexibility when it comes to choosing a closing date.