I went and looked at the pattern for your hat. The bill is made separately and then folded, lined with the plastic and sewn on the hat you made.
I don't understand your first question. You cast on with any cast on you like to use and the row 1 they give is a right side row so it will be knit. You are going to work the brim in St st, so one side will be the smooth knit side and the other side the purl, bumpy side.
All the rows from row 1 until you have incorporated all 40 stitches into your short row shaping are short rows. Short rows are rows that are turned before you have worked clear to the end of a row like you normally do before you turn. Rows 1 to 4 that are given are all short rows but you keep working in the same way adding 3 more stitches in the middle each time before you turn until you have worked across all 40. In other words you will be doing the following: (the knit rows are the right side and the purl rows are the wrong side)
Row 1: Knit 25, turn. (exchange the needles [or needle tips if you are using a circular] in your hands like you would at the end of a row, so that you are ready to begin the next row working with the other side facing)
Row 2: Slip 1, p12; turn.
Row 3: Slip 1, k15; turn.
Row 4: Slip 1, p18; turn.
Row 5: Slip 1, k21; turn.
Row 6: Slip 1, p24; turn.
Row 7: Slip 1, k27; turn.
Row 8: Slip 1, p30; turn.
Row 9: Slip 1, k33; turn.
Row 10: Slip 1, p36; turn.
Row 11: Slip 1, k39; turn.
Now work 6 rows with no shaping keeping the stockinette going and working all 40 stitches each row.
Then you shape the other side of the brim by doing bind offs at the beginning of each row as follows: Bind off 2 sts at beginning of next 10 rows-20sts are left at this point. Bind off 3 sts at the beginning of next 4 rows-8sts are left. Bind off the 8 stitches.
The finishing tells you how to finish the bill. You fold that piece you just made in the middle, so that the fold line becomes the front edge of the bill. Insert the plastic and then sew the two edges together. Then sew the sewn together edges onto the hat in the center front.
Cute hat. Your sister will like this.