I’ll answer the easy one. If you are knitting on straight needles (as opposed to knitting in the round), then yes, you seam up the back when you’re done.
The matter of gauge–each size needle and yarn combine to create a stitch of a certain size. The variation comes in with the knitter making the stitch. No two people knit exactly alike–some are tight, some are loose, some are in the middle.
When a pattern tells you a gauge for the piece, it’s the number of stitches per inch that were used to write the pattern and come up with the measurements for that pattern. If you knit tighter than the designer, you’re hat will be smaller, looser that the designer, bigger.
What you do to determine your gauge is to knit a swatch–usually a 4x4 piece with the yarn and suggested needle size. Then you count how many stitches per inch you get compared to the pattern. If you get more st per inch, you need to go up a needle size/too few, go down a needle size.
Gauge doesn’t matter too much in scarves and blankets, where fit isn’t important. And to be perfectly honest, I wouldn’t knit a swatch for a hat. But if you find that you are a very loose or tight knitter, you may want to make sure you are at least in the ballpark.
For things like sweaters, gauge is more important. For example, if I am making a sweater back that has 100 stitches and I knit 4 st per inch, my piece will measure 25 inches. If my gauge is 5 per inch, my piece will measure 20 inches.
Sorry for the long post–got carried away, here.