You're shaping the neck which is lower in front than in the back and is a bit wider, so you will be making more rows and end up at 8" before you begin the shoulder shaping. Follow the instructions as given and it will make sense when you get there.
Usually one washes and dries it after it's knit up, it's a pain to do it beforehand. The itchiness may be a reaction to the 'sizing' that is sometimes put on yarn, just like clothes and needs to be washed out. I've never had an itchy acrylic wouldn't expect to from the yarns sold at Walmart which I've used. Most people advise a gentle cycle and low dryer heat, but I just put acrylic knits in the regular wash (with something light, like t shirts or other knits) and a regular dryer setting. But I do check the dryer after 20 minutes or so and take it out as soon as it's dry. Too much heat can make it limp. You could make blankets with it, double stranded on huge needles will use it up faster. It can also be used for a cardigan or jacket, something worn over other clothes. Try washing and drying that hat again and see how it feels then.
Knitting in the round when you have a number of stitches that won't divide by the rib pattern, dec or inc so that they'll fit. For a cast on, yes just CO the right number, then you may want to add or take away more at some point if the ribbing is not continued all the way up.
When you have a stitch number that isn't divisible by 4 for a 2x2 rib, you can handle it 2 different ways: either k2, p2 across and end with k2, or you can k3, then p2 k2 across, with the extra knit at the end of the row. If this is going to be seamed, then you can decide which would look better after it's sewn up.
The main thing though is that you can't do the 2nd row the same way. The back of a knit st is a purl, the back of a purl st is a knit. After you do the first row, you need to turn your work and look at how the stitches appear. You would knit the knits and purl the purls, so if the next st facing you on the needle looks like a purl st you would purl it, and if the next stitch appears as a knit, you knit it. Do this on every row after the first one and you don't have to keep track of it being a RS or WS row. This also works for knitting ribbing in the round.
For gauge I'm supposed to have 26 stitches and 40 rows per 4 inches. I knitted a swatch in the pattern on 3mm needles as suggested. However, I've got 33 st per 4 inches and 23 rows? Apparently row gauge is important for this - is my yarn too chunky? Going up a needle size will probably fix my stitches per 4 inches (last time I went up a whole needle size and got the right stitch gauge - I think I'll probably try knitting a swatch with 4mm needles to see how I go.) However, if I go up a needle size, I'm going to have even less rows per 4 inches won't I? Should I just not worry about the row gauge?
Are you sure you're counting the rows right? It sounds like you need a couple sizes larger on the needles for the stitches. Try that, then wash and dry the swatch like you will the sweater; you could stretch it a little wider which will take up the length. The row gauge might not be that critical, you can probably fudge it, but that's if you were getting much closer to the gauge. Looking through the projects on ravelry, many knitters had trouble with the gauge, though they were getting something like 36 rows.
A baby hat is usually about 14-15" around, though a loom can be a little larger. There's a loom knitting group on ravelry who can offer a lot of help - http://www.ravelry.com/groups/loom-knitters If you're not a member yet, it might be an idea.
Yeah, knitting doesn't unravel well from the CO and with ribbing you have to pull the yarn through the sts because of the alternate knit/purl. You can cut a stitch just above it and put the sleeve sts on a smaller needle as you take out the yarn. Then either reknit from the old cuff if there's enough to do a full cuff, or use the leftover yarn.
Superwash won't shrink, though putting it in the dryer will take it back to its knit size, so if you just washed it and laid it flat to dry, that could help. If that still turns out too large, you can try the fleece, or weave some elastic thread through the lower edge to tighten it up. If you knit the swatch flat, you may knit looser than you purl, so when you knit in the round, there's not purls to tighten it up. Also check that the finished measurement you thought your wanted wasn't too large; a hat should usually be a couple inches smaller than the head measures.