What is this white textured paint-looking stuff on my concrete floor?
Your first picture looks like the concrete floor just had carpet installed on it. The white paint around the edges is where the builders sprayed primer on the walls and baseboard and spilled a few globs in the process. The dirt just looks like construction /drywall dirt along with dirt that fell in the cracks over the years.
Your second picture looks like that part of the floor was definitely covered with vinyl or sheet linoleum and was glued down with a mastic adhesive.