Since I don't see it mentioned, I'll add that it's important to use the grain lines as they were in the original. You should be able to see if the fabric was cut on bias or not. Patterns we buy have arrows to indicate how pieces are to be placed on the grain, and I would do the same - find the grain and use a ruler to mark it on your pattern, which you should make out of non-woven interfacing (so it will hold up and be worth your effort). I would also use the same type of fabric, whether knit or not, and if knit, one with a similar amount of stretch.
Also, unless there is something unusual about the piece, such as a folded in facing, there is no need to pull the stitches of the item you are trying to duplicate (unless you plan to sew it back together!). Just cut as close to the edges of each section as possible and add the 1/2" seam allowance to your pattern. That should be much easier.
Set in sleeves are much easier to sew if you sew the shoulder seam of the garment, then sew on the sleeve without sewing the sleeve seam, and finally sew the side seams from the bottom edge all the way to the end of the sleeve. A lot of patterns have you actually set in the sleeve after the side seams are sewn, and that's for the birds!
Good luck!