depending on the size of your loan $3K might be okay. Ask where the closing costs go. Insurance and fees are can't be avoided and no, you don't have much choice about points. However, some lenders will lower the points but it is usually at the cost of the interest rate.
In all honesty, loans are cheap right now. Our first home loan was at 8% and when our friends bought homes a few years later it was up to 12%. And even then, think what credit cards and car loan interest is. Much higher than 4%. And remember the interest on a home loan is tax deductible for federal income taxes. So it makes the interest cost even lower depending on your tax bracket.
If there is anyway to make a higher payment, everything over the regular payment goes towards principle and you pay it off sooner.
Remember, I'm an interest nazi. Not exactly sure why, but I hate to pay interest. When we bought our first house, my aunt told me to never take a second mortgage. It stuck with me but it does make sense if you can get an overall lower interest rate.
When you apply for a loan, at some point you "lock" in an interest rate. If you locked, the lender has to give you that rate. But locking in the rate is a risk for both parties. You might lock in at 4% and it goes down to 3.5% the next day. Not all lenders are crooks. Or so they say 
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