Mortgage pre approval questions

[Anonymous]

When a lender pre approves you for a certain amount can you go over that with a down payment?  So lets say the lender says $240,000 and I am going FHA which requires me to have $9,100 for a down payment.  If I put $10,000 down can I buy a house that is $250,000?

Also, I thought that within the 1st 30 days of applying for mortgage pre approvals you can do as many as you want and Fico won't ding you for all of them.  I had a lender tell me depending on our credit score more than 4-5 drops your score.  Is that true?  Thank you!!

[H-B]

If you stay with your current lender, most of the time they don't pull your credit for 6 month so its won't effect your score. Yes you can pay the difference if you are not approved for higher loan amount. But most of time $10000 is not going to make huge difference in your DTI because payment amortized in 30 years. Its property taxes, HOA fee and insurance which impact a lot on DTI.