Hello! First, you should go back and edit your post to just provide the link to the pattern. Posting entire patterns is a no-no due to copyright issues.
To answer your questions--
Patterns often say that the stitches on each edge are edge stitches because those are the stitches that are used for seaming, and they aren't generally included in the finished measurements. Just knit them as the pattern instructs.
As for the gauge question--most patterns have a caution to check your gauge, or pay attention to it, etc., because if you don't your tunic will come out the wrong size. This is usually put before the instructions start, but my guess is that it is included within the instructions here because Drops patterns are translated into English, so the language isn't always as precise in the English versions of the patterns.
ETA: Forgot to answer your circular needle question--No, there isn't really anything different for this pattern. You aren't going to use them to knit in the round--they just call for a circular needle because you have to cast on so many stitches and they won't fit onto straights very well. You just need to work back and forth and turn them at the end of the row.