Upholstery and egg crate type foams will not be rigid, and may not be flame retardant. EPS and XPS construction insulation foam are lighter weight, more rigid, and could be covered with batting and fabric. They come in 4'x8' sheets, but can be cut with a utility knife into smaller sizes. They are available from a big box home improvement store like HD or Lowes. Not sure if they are flame retardant. Depending on how large a piece you are mounting, I would think they may be light enough in weight that they could be mounted to the wall with 3M removeable hangers of some sort.

Is the indent in the wall where you have the TV now, supposed to be for a TV or is it to be a closed up closet?? You could switch the room with living area where you walk in but then you cannot wall mount the TV due to windows. Plus you might like eating near windows for more lighting drama. Also , now seeing your hall , I think turning the dining table 90 degrees from how I placed it, would fit better in your space. You could consider an area rug under the table as well , which would help to define the space when you enter. Also keeping a runner and a vase with either fresh ( or nice fake) flowers on the table, will make it flow better with the living room area furniture.

For the dining room, I think I'd orient the table 90 degrees from how it's drawn, and I would make it a drop leaf or gateleg table so that it can be made smaller when not being used for dining. I would embrace the idea that the entry is right in the middle of the living room, and bring the living room furniture out towards the fireplace so the fireplace is connected to the seating area. Maybe TV above fireplace. In that back corner where the sofa is drawn, I'd make that a small work/office space.

Check the layout . It is made to the scale so that every necessary requirements can be incorporated as per the dimensions .The only structural change mentioned here is the balcony door , which is shifted on the corner and rest of the wall is changed into a big window for the natural light which helps in additional sitting and if you want to develop some greens in the balcony the view from your living room will be just perfect. In the kitchen area there's a breakfast table with hanging display to bar the direct visibility from drawing hall . All the measurements are given to the scale.