You don't need to purl on circular needles as the same side is always facing you. With normal knitting you knit a row, turn the knitting over to do the next row, that's why you need to knit one row, purl the next row.
Doing a small sample of knitting in the round is actually quite tricky - in fact a hat normally is a small sample, if you see what I mean! You can do a gauge swatch for a project knit in the round like this (basically, knit a row of stitches, then push them back up to the left hand needle again, leaving a long bit of yarn in the back so they don't pucker). All in all, I'd just crack on and see how you get on.
You don't have to switch to DPNs when the work gets small, although you might feel more comfortable doing that if the pattern has very clear instructions to do so. Have a look at magic loop. This is a bit tricky to do with a short circular needle, like a 40cm that you'd be using for a hat, so you'd want to switch over to a longer one.