Take a utility knife and cut along the edges of the wall and the ceiling which will stop the drywall from any kind of wear or tear during the demolition.
Then, make a hole in the wall and check what kind of wiring is behind it. After inspecting the studs and electricity, you have to move to the wall which is between the dining room and the kitchen. You can consult with any licensed contractors about re-wiring and re-directing the pipe work.
Now, take a hammer and remove the drywall. Moreover, you have to take all the nails out of the studs. Then, make a frame for the breakfast bar with the dimensions of 2x4s and install the drywall on both the corners of the frame by the help of studs.
You will have to make the base for the cabinets with the same dimensions i.e. 2x4s. Besides, make sure that the base is levelled. After that, place the cabinets in the right place, clamp them and screw them.
Cut the plywood by taking the right measures and paste it around the bar. Use good quality wood stick to paste it properly.
You can use a roller to apply the adhesive on the plywood. You have to add a thin coat of adhesive to the laminate. Then, place the dowels over the top of the counters. Now, lay down the laminate over the dowels and pull them out afterwards.
Your breakfast bar with storage is ready, just trim the edges of the laminate with the router.