Do all teeth have some movement when pull them?

Yes they can but if : They move more than .5 mm that can be a sign of something more serious...Periodontal disease or hyper occlusion . Teeth are attached to the bone by periodontal ligament fibers or sharpys fibers. When to much pressure is applied they can become injured and sore like a sprain ankle. Bruxism and clenching can stretchand compress them and damage bone supporting teeth leading to greater mobility.

Yes: There is slight movement to all teeth. If your not sure that yours is normal have a dentist check them.

Yes: If your teeth are healthy this movement is almost unperceivable. It can be as much as one half mm movement front to back and side to side. If your teeth depress at all into your jaw bone then this is a sign of gum and/or bone infection and should be evaluated by a dentist immediately.