Who are the strangers in your dreams?

You're not crazy. There is a bot working behind the scenes.

Experimenters have shown us that electronics are an order of magnitude faster than neurons at making connections, so --- how is the brain so fast?

Think for a minute about how many things you can do at the same time. Think harder, and you'll notice that with training, the brain can estimate an original premise, then modify all the arguments which depend on the premise on the fly. You can see the immense powers of abstraction the brain has merely by listening to music, observing a work of art...
...or acknowledging the immensity of a project resulting from a simple question: "What do I need to do to put somebody on the Moon and bring them back?"

So, the brain is capable of forming multiple pathways on the fly to solve a problem it has become responsible for solving. One can even enlist the aid of other, like-minded brains to work on the nuances of any problem suited to them.

"OK, genius, get to the point," you said. OK:

You have an avatar in your head for every person you've ever cared about, and this avatar can be considered alive.

You use the general pattern of behavior you have observed in others, as manifested in these avatars, to endow images of persons you've never met with imagined behavior patterns.

Immense abstractive power is present in the alert individual to predict adverse conditions, such as attacks offered through the environment. Be it weather or a rival tribesman, the brain can figure out ahead of time what might happen, and prepare. 

This is a survival trait.

You have an innate power to recognize hazardous conditions, and your memories are both extensive and non-verbalized due to their complexity. You have extensive memories of normal human behavior, a sort of Identification, Friend or Foe, and specific memories of the significant people in your life. You remember what they look like, how they walked and talked, how they acted, what they smelled like at different stages of their lives. This also includes other conditions like those found in your neighborhood and car. The sound of rain on the roof. How the lawn smelled when the dew fell.

There are thousands of scenarios you can consciously recall, and others waiting to be brought out into the open by a trigger of some kind. Can you say, "deja vu"?

It is a trivial thing for your brain to populate any dream with realistic people because the rules for normal human appearance are ingrained. The mechanism is the exact same thing that has you running from a poorly-lit shape in the night.
That rule is: unfamiliar = threat.
The rule in your dream is: "People look like {this}."
The rule for a person about whom you fantasize is: "Person should act like {this}."

There is more!

All the loved ones that have influenced your life are "indexed" in your mind well enough that you know, not only what they look like, but what they would say or do given any particular situation.

Your eyes take an image to be processed by the brain, and the visual cortex is huge. 
You know about optical illusions. Magicians know dozens of ways to fool your brain with physical illusion. Why would you think you actually have to see something for the brain to work with it?

Grandma isn't seeing ghosts. Her memories are so intense that she can see her memories vividly by contrast with the tamer life she actually leads. She wants desperately to see the people and do the things she remembers.

The power of abstraction is so large that people frequently substitute fantasy for reality in order to feel better, because learning, basically the integration of reality into the mind, is often unrewarding, especially when compared to the comfort we imagine seeing our loved ones bringing. 

As long as we remember the difference which ALWAYS exists between reality and our perception of it, we can avoid costly mistakes.