I did a gentle blow out with a blowdryer once and it looked decent. I never straighten my hair.
What I mean by crazy is that you hair will start to not look as good as it originally did immediately after the cut. After about 4 months or so I noticed that I needed more product - wash and goes were more challenging. My hair tangled more.
As far as growing it out. Each person is different. I will say maybe it took a year or more for the entire cut to grow out. These are internal layers.
Your hair will never look as it did prior to having the Ouidad cut, which I don't see as a bad thing, but after a few months (4 for me) of having the cut it won't look as good as it did immediately after having the cut.