Most my doors were already here, but I did have one moved over, about 6 inches. However, the entire space was demo'd, and rebuilt, so that's not the best example to draw from. If you want the door hidden, in a pocket, yes, you will need a skilled carpenter. Essentially, the opening header and frame, will become twice it's size, with the "pocket" part, hidden behind the wall. The studs/supports will need to be removed to make a space for the door to slide into. Do you have any switches or outlets on the fireplace wall?

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.

There are several variables in estimating the cost of renovating/decorating a home. If you are not structurally changing your home then an architect is not required. If you are doing the work yourself then cost comes down to the materials you want in your space ie: hardwood, tile, laminate etc. If you are not doing the work yourself then you need tradesmen ie: flooring installers, painters, drywall installers etc. If you are looking for someone to organize all your reno's then you may want to hire a general contractor. Using Houzz Find A Pro tab you should be able to find professionals in your area. Good luck with your project.

Depends on what needs the sound proofing. I can't explain Acoustic Drywall if you want to insulate the floor. I can't talk about floor underlay if you want to insulate a wall or a ceiling. What you are trying to achieve (one room or an entire home) and what your expectations are will also decide "best" way to add acoustic insulation. The "Best" way to do it is to BUILD IT properly (with the acoustic materials used from the start) with acoustic materials. The "worst" way to do it is to retrofit the acoustic insulation at a later date.