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A lot more information to cover here in order to help you. You mentioned FHA, so I assume you were approved for 3.5% down? It seems perhaps you might not understand that closing costs and down payment are completely separate things. The seller will pay closing costs but you are still responsible for the 3.5% down payment. So yes you would still need the funds. DU simply checks your credit score meets the minimum requirements.
An underwriter does not "challenge" DU findings so to speak, they just need to do things a DU system cannot. This is things such as verifying your income source, verifying your down payment funds, looking through bank statements to make sure there are no other debts you didn't specify. So as the other poster mentioned getting approved through DU is a great first step but there will be other things that need verified to be fully approved.
Good luck!