Sorry. There's not enough information here for anyone to answer your questions helpfully.

Yes, it is a lot of work. You need to either get a pre-fab shower pan that is already sloped or you have to hire a tile professional to build a properly sloped floor onto your space. You also need to have plumbing to the new shower drain and water supply and any shower heads. Then the walls either have to be a prefab set (like acrylic), a solid surface (like Corian, Swanstone, Transolid, Kohler Choreograph...), or must be waterproofed along with the floor pan before tiling. This is a very simplified list of what is needed, in truth it is more complicated. But you do need to look into prefab showers or solid surface showers or tiled showers and decide what it is you want. You need to have access for a drain and the plumbing.

Thank you both of you for your comments.

The closet already has the water supply and plumbings for the washer including an overflowing drain pipe.

there is a duct for the dryer.

The walls would be tiled.

You will need permission from the board. All of those pipes belong to the building, not you. You will need an expert liscensed and insured contractor who understands proper waterproofing. You will need 10K minimum. More if you want fancy.

NYC condo's and coop often have rule that requires wet over wet only. There are exceptions but permits must be pulled and your contractor must meet all the building department requirements. This link may help you begin to understand all the steps involved. Here is another article that is written by an architect. Good luck.