Yes it is possible; we did it four years ago but I do not remember how long it is.

We drove up to hike the Tower. I believe we saw a family hiking a trail towards the tower from the campground. Check out the nps.gov website for this National Monument for more info.

Quick hike, maybe 30 minutes. The hike around the tower was actually longer.

Yes, the trailhead at the campground is located near site A15, you will pass along the edge of the Prairie Dog Town, then cross the roadway. The total distance from the campground to the Devil's Tower Visitors Center is approximately 2.2 miles one way. The elevation gain is about 700 feet, it's a moderate hike with great views of Devil's Tower, and the trails are well marked.

Yes it is! South Side Trail out of Loop A and then left on to Red Beds Trail will get you there. Maybe a mile and a half?

Yes it is. You can walk to the tower and around the tower. I can’t recall how far, but not very.

Yes but the visitor's center is on the other side. It's not that far though

Not really - it's quite far and you have to walk along the road. I'd recommend driving to the visitor's center and parking, then taking the trail from there.