If you're going to use a circular, I would use the shortest cable possible, like 16" or something like that. I've made dozens of these for adults and used a 20" circular with no problem. Although come to think of it, I do have to switch to the dpns by the time I get past the first couple of decreases. Were the purl stitches the only ones that gave you problems on the pants? Because the only place you'll need to purl on the hat is in the ribbing-- because you're in the round, the rest of it is all knit. Hmmm, I'm wondering why your purling is very loose with dpns, because it's so much like using a circular, except you keep changing needles. Are the of the same material as your circulars? And when you get to the decreases and divide the work into quarters-- great question! I didn't word it very well-- you just divide the number by markers, or once you've made a couple, you might even be able to get away with just visually keeping track. You don't have to use 4 needles to divide them onto, but there would be nothing wrong with it, and if it helps you keep track of your quarter sections, then go for it.
As for the pom-pom-- I've made them, but not for this hat, specifically. I didn't even check!-- do they include directions for the pom-pom in that pattern? If not, you can find one on line pretty easily. They make these plastic disks things for making pom-poms, which I've found very helpful. All you would do with the pom-pom, is make sure that you've got 2 tails about a foot long-- one from where you started and the other from where you finish it. Then with a crochet hook, or threading the tail through a needle, at the very top of your hat, pull one of those tails from the outside to the inside. Then go over a couple of stitches and do the same thing with the 2nd tail. Tie them together inside, making a couple knots so that they don't come loose (you KNOW she's going to pull and twirl that pom-pom:) ) and then cut off the remaing bit tails, leaving about an inch.
And last but not least-- I just posted some info about basic mittens patterns. The one from the vintage site, which is the battered one I still use all the time, has a great pattern called "Classic Mittens and Gloves for the Entire Family", kind of charted out by size the way the hat pattern I recommend is. And you can knit them flat or round, they give directions for both. Now those, if you do them in the round, can only be done by dpns. And if you decided to either that hat or these mittens from these patterns, I've made both loads and loads of times, in all sizes, so I can REALLY be of assistance. And how are the pants?!