Hi and welcome!
The easiest way to do the cast on
is to turn the work, that is, take the needle with the stitches in your left hand and use a knit or cable cast on for the 3sts. Then you're ready to purl. For the increase you can do this increase
at the end of the row. If the increase at the end of the purl row repeats in following rows, this increase will work. For this particular increase in row 2, you could also just cable or knit cast on 4sts instead of 3sts.