RE: do deer stay in the same place
Depends on allot of factors. In general: Most deer (per books) have a specific territory are rarely leave it. But deer will travel far if chased by dogs or some other extreme pressure. Rutting bucks can put on miles too if there is not allot of doe in his area.
Usually if spooked by a hunter and they havn't been pressured too bad, the deer will only run a few hundred yards, thenstop and watch/listen.