Helicopter, Tricopter, Quadccopter - what's really happening here? Are there generalized advantages on a small scale? There have been, it seems, a proliferation of quad-copters commercially available.  Amazon seriously tried to use them for deliveries.  (Search Drone on their website.) The NFL uses one for cameras.
There are dual bladed copters (helicopters!) triple, and quadruple bladed vehicles available.  However, does any of these designs have inherit advantages?
Is one inherently (or often) more stable?  Are any of these designs more energetically efficient than the others?   Does one scale more robustly with load?
It's easy to imagine loose mechanical analogies for the behavior (stability) of one or two bladed vehicles - I know what a stool is (for example.)  However, the closest I got to seriously studying fluid flow was Engineering Mechanics II.
I actually want to understand what's happening.  Can the quadcopter use weaker blades, since it has four working together?  It seems power consumed would rise faster than efficiency...
Thanks in advance.  I may or may not understand derivations, but it would be cool to see results that describe what's actually happening!  I'd love to build one on a hobby level.  
I'll be appreciative of as much detail as you can throw at me - I have a few days off and others might like it too!
 A: If you just give something one rotor it will spin out of control. On a helicopter there must be either a small second rotor or some kind of control surface that uses the wind generated by the rotor in order to counter the torque. It also needs to be able to increase or decrease it, for if you do want to spin the helicopter, and it needs to be able to generate torque on the other axes in order to stabilize it. You only need one rotor, which probably makes it cheaper for big ones, but it's complicated.
If you have four rotors, it's much simpler. You have two rotating clockwise and two counterclockwise. That way, there's normally no torque. If you want to turn clockwise, you slow the clockwise ones and speed up the counterclockwise ones. Reverse that to turn counterclockwise. If you want to lean to one side, slow the rotor on that side and speed up the one on the opposite side. Since those are both spinning in the same direction, it doesn't add any torque.
A: You are talking about blades, and then you are talking about helicopter/bicopter/tricopter/quadcopter. That's two different things.
The blades refer to the number of "wings" on a rotor, and the heli-/bi-/tri-/quad-copter refers to the number of rotors.
I'll answer both questions:
Blade count
Having more blades will give you more thrust at a given rotational speed (since there are more blades pushing down air), similar to having bigger blades. But they also create more turbulence that the other blades are slicing through, which reduces the overall efficiency.
So basically, more blades allow you to reduce the diameter of the rotor, but also reduce the efficiency.
Most efficient would be a large, rather slow moving, single bladed rotor (google them, they look really trippy). But having more blades allows you to make smaller rotors, so that's what's done most of the time.
Rotor count
Having less rotors allows for higher efficiency. But:

*

*Having an uneven number of rotors creates torque. That means, for example, if you don't counteract it, a helicopter will start spinning out of control. That's why they usually have a small rotor on the rear, that counteracts that rotation.

*If you have less than three rotors, you cannot fully control the aircraft using only the rotor speed. Helicopters need a rather complicated motion system to allow the helicopter to pitch, yaw and roll. A Bicopter needs to be able to pitch it's rotors to control it's motion.

*If you have less than six rotors, you don't really have redundancy. That means, if one rotor stops working, you can't fly anymore.

Why are helicopters chosen for human-sized aircraft and quadcopters for small things?
Human-sized aviation
In human-sized aviation you usually use fuel-burning engines, because of the energy density. These engines usually can not change their speed quickly. That means, you will need to have complicated mechanics anyways, so might as well use the more efficient helicopter design. Also, compared to the rest of the size/weight of the aircraft, the mechanics aren't that big or heavy.
Small scale aviation
In small-scale aviation you usually use electric engines, and space and weight is at a premium. Electric engines can speed up and slow down very fast, so controlling the aircraft only through RPM is a big advantage.
So, as said before, the lowest even-numbered rotor count where you can do that is a quadcopter. That's the reason quadcopters are used for non-critical applications (toy drones, small camera drones, racing drones, ...).
For more critical operations (for example a heavy-weight camera drone that flies over an audience), six or eight rotors are usually chosen, sometimes even more. That gives redundancy and helps to avoid scenarios like this one:
https://www.youtube.com/watch?v=uJwot3T9EOA
(To be honest though, this one was caused due to a control malfunction, not to broken rotors)
Human-sized quad/hexa/okta/.../copters
Currently, there is a boom for flying-car-style multicopters. These are a bit of an investment scam, since, compared to a helicopter with otherwise similar specifications, they are very inefficient and smaller rotors usually mean, that they produce a very loud, high pitched whining noise.
Don't expect any of those over your city anytime soon.
Common Misconception
Many people believe, that quadcopters are easier to control than helicopters, since they played with non-computer-assisted helicopter toys (which are very hard to control) and computer-assisted quadcopter toys (which are really easy to control).
But the difference is the computer assist. Flying a non-computer-assisted helicopter is difficult. Flying a non-computer-assisted quadcopter is borderline impossible.
