How to secure a jack wall to an existing wall?
You have to notch your roof rafters (birdsmouth) at the bottom and at the top so that the rafters can sit on the plates. You'll then nail from each side to secure it to wall plates. Familyhandyman has a diagram on what this is.

For the jack studs, you'll need a top and bottom plate for it so you can nail/screw the bottom plate to the top plate of the existing wall.

Once the siding, roof and rafters are put on it'll be secure. I live in a hurricane prone area and I built my shed similarly and it has so far withstood a few hurricanes.