No one who replied to you has actually run down a deer, or any other animal for that matter. In fact, it's obvious that not one person that replied to you has actually ever been hunting. Therefore, not one of them is qualified to answer you.
I have run deer down and killed them.
Yes, you can run a deer down and kill it with a blade, be it spear or knife. I prefer the knife. It puts me in direct contact of holding the animal down. I position myself behind the neck of the animal, rest one knee on its shoulder, one hand on its head. With my other hand I take out my knife and lay it on the ground in front of the deer, and then gently stroke it under the chin until it starts to relax. When I feel the moment is right, I pick up the knife, line the blade parallel with the spinal column just ventral (towards the front part of the body) of the spinal column. In one quick motion I slide the knife in all the way through the neck, twist it so that the blade then faces ventral, the pull it forward (away from me) through the trachea and esophagus, opening up the whole neck. When done correctly, the animal dies instantly and you will not get any blood on you.
You want to know about the run. Yes, you can do it through the woods, through fields, up hills, down hills, across creeks. It only becomes too difficult through dense brush. Deer can move through that where we as humans have trouble. How long? Well that depends on many things. Just over an hour was the shortest I have done, but the deer slid on some mud and I caught up to him. They usually overheat in 4 to 5 hours max. You don't need food or water, just focus on your breath.
If you're serious about it, it can be done, and it's the most rewarding way of hunting, and it's worth it. For the record, a 120lb deer will give you about 35 to 40 lbs of meat, not 55. Nor do you need people and radios and all this other crap. You need focus. You need determination.
Take some tracking classes. Take some hunting classes. Learn to butcher. Learn to brain tan a hide. Learn to make sinew. Learn to make hoof glue. Listen to birds and learn how they warn animals of humans and other predators. Learn how to broil deer ribs to perfection, make the perfect backstrap, braise the shank in garlic. Go and scout the area out. Choose a deer and get to know everything about him or her. If you really want to do it like the ancients, you can learn envisioning and meet the deer you will run down. The Bushmen are not the only persistence hunters. There is a long tradition in American Indian culture, and many anthropological studies have been done. You can even look up a course called "Guardian Intensive" at Teaching Drum in Wisconsin. Control your mind. Go have fun!