I had a crown braid done last summer.  I was able to keep it for a week.  I did rinse my head, but did not wash it, in order to minimize the fly aways.

I believe there are products out there specifically for cleaning the scalp when you have the close braids.  Can you ask the braider for advice?  They might know what would work for you.  Caucasian hair is very different from "black" hair, in that it is usually more slippery, less curly and therefore more prone to coming out of the braids.

I was told to wrap my head in a silk scarf at night for sleeping to help keep the braids neater.  Although that didn't work real well for me, I did find my satin pillowcase helped alot.

I hope you have fun with your braids and they last a long time.