Haunted house?

No!

It is the faculty of the spirits of demons to manifest themselves to whom they wish, they can show themselves to some people, and to others not!

If you have a residual haunting (a replay of a past event) a person may be seen to walk through a door that no longer exists but did so at another time. If the neighbour's house was once part of your own house, then people next door may also experience the same. My pal would often hear a child running along the upstairs passage and even managed to see him a couple of times but only from the waist up. It was later discovered that a 17th-century barn stood on the site of his house and the child was burned to death in that barn on a floor that was a little lower than his own floor.

Absolutely, especially if on the site there was previously a grand house which has subsequently been divided into smaller apartments, the ghost may not recognise the new barriers. 

It depends if the spirit is restricted to that property or is from the area or land that the property occupies.

So, uncle Burt may just occupy his old house, while a car crash victim wanders around a bit so may show up in any local houses, and an old Indian may consider all that land as his.

It depends on the next-door neighbors. If they are as silly as the haunted house owners, it's very likely they'll experience paranormal activity (they may have already). If they are critical thinkers, then it becomes very very unlikely.