Velvet has a nap and is directional. Position pattern pieces so the smooth side of the velvet runs down the body. If you use some one way and some the other, it will reflect the light differently and can look like 2 totally different colours (unless that is the look you are trying to achieve).
Velvet is more stretchy than swim/spandex fabric, 90-100% stretch vs 65-75% stretch. You may need to size down depending on the pattern you are using and the fit you are aiming for. For all of my children's clothes, I make to the same size and just expect it to be slightly less fitted.
To keep the same finished lengths for bindings, it is necessary to reduce the binding length a little. Swim/spandex fabric binding lengths are typically around 90% of the opening, where velvet is around 80%. For BOO! patterns where neck binding is used, this would mean reducing neck binding by around 4-6cm (1.75-2.25") across children's sizes.
When overlocking velvet, increase diff feed. I have mine set to 1.3 for swim and 1.5 for velvet (and stitch length around 2.5).
When coverstitching velvet for top stitching and hemming, I set diff to 1.5 and stitch length 2.5-3.0. I use stretch thread in my coverstitch looper and set tension on that to 0-0.5.
While you absolutely can leave velvet unhemmed, it may curl a little over time. My preference is that the hem of dresses and tops are finished when made with velvet. For circle sleeves and flutter sleeves, I don't hem as I feel the hem creates too much weight on the sleeve and you loose some of the fluidity.
To hem velvet, create a stay stitch along the hem by stitching 1.5cm from the edge with a sewing machine. This will ensure the hem doesn't stretch out of shape too much when stitching and also form a perfect stitch guide for folding up the hem. Set stitch length to the maximum number and decrease the tension (I set my stitch length to 5 and tension to 2). I don't use pins or clips when stitching the hem, just keep stopping and adjusting to fold the hem under using the stay stitch guideline for folding the hem. I generally use wide needles when hemming velvet. Remove the stay stitching at the end.