Won’t that get in the way of the bed more than the shelf? Talk about horny!!
Regardless, I would match up the studs above and below. Two suggestions: cut the scab-in studs maybe 1/16” too long so you have to set them in at an angle and then tap them into place vertically to restore strength (not pound them in). It’s probably not a structural wall, but if you make it very tight, you won’t have to worry about wall cracks and such when you’re pounding the headboard against the wall (when you’re moving your furniture in I mean).
Along the same thinking, instead of toe nailing them in, get a handful of long wallboard screws, pre-drill the holes a little smaller, and then screw them in. You only need two screws per stud, one from each side, above and below, and that way you won’t crack the sheet rock with the hammering. It’ll only take you 10 minutes longer. An alternative is Liquid Nails construction adhesive and no nails screws. Put it on the ends and the frame before you tap them in.
Yes, use insulation, it’s not just about temperature, it’s also about preventing condensation (and mold) inside the wall.
Finally, if you talk to a couple local contractors or sheet rock guys, they can probably tell you how they created the texture. I suspect it might be as simple as mixing up a little thin spackling paste, cutting it with a little water, and then running a long hair roller over it. Or maybe the use a stipple brush and then sand the peaks gently when dry.
Second finally, Instead of taping it like a regular sheet rock joint, use some high-quality caulk, so you disturb less of the wall. It will become invisible when you put the texture on.
Third finally, when you texture the edges, don’t carry them across and up and down in a straight line. Run the line in and out, like a starburst, like you would feather paint on a car, and you should be able to make it invisible to anyone who isn’t looking for it.
My 2 cents, hope it helps.