Only if the room is cold or the AC is running. Bare feet are actually better for a newborn most of the time, they're not moving yet, so there's no grip or support needed. Socks that are too tight can also restrict circulation in feet that small, so if you do use them, make sure there's no elastic cutting into the ankle.
Yes, indoors especially. The foot learns a lot from direct ground contact, texture, temperature, pressure, and that sensory feedback is part of how balance and coordination develop. A baby navigating a tile floor barefoot is getting input a shoe sole would just block. Outside is a different story, but inside the house, bare feet win.
Once they're walking outside on their own with some confidence. Before that, pre-walkers or bare feet handle everything fine. The moment outdoor surfaces become part of daily life, hot pavement, uneven paths, dusty parks, that's when a proper pair of shoes earns its place.
The right pair barely interferes at all, which is the whole point. Well-fitted, flexible shoes let the foot move naturally and the muscles do their job. The problems start with stiff soles that prevent the foot from bending.
