You should be able to weave them just by twisting the carried yarn around the working yarn once at the end of a row.
As far as attaching the blue, you'd be doing Intarsia (video in advanced techniques) where the blue meets the stripes. The stars would be fair isle. Use a different piece of white yarn for the stripes than for the stars.
Yes it will curl. Will it be sewn to something, or backed by something? If not, then what about doing the stripes in garter stitch? Just make sure that the stripes are an even number of rows (there's 4 rows, right? hard to see the pic), and that you do the color change at the beginning of a RS knit row. Otherwise the two colors will overlap (as you'll see on the back of the work). Only complication would be the height of the star section taller than the stripes if only stripes in garter. Might be worth trying though. Just a thought.