Yes. Closing costs can be negotiated between buyer and seller. Buyers can request seller credits, and sellers can offer concessions to attract buyers. Some fees (like lender or title fees) may also be shopped around for lower pricing.
Closing costs and down payments are 2 different things. Your lender will itemize them for you. Some loans allow sellers to help with your down payment, but most loans do not. A good lender will also look for grant money for you. Your lender is enormously important in this transaction. They can cost you or save you quite a bit of money. Choose wisely! Your Realtor can help you with that.