I would like to know if a prop plane, for example the P-51, could be able to fly backward. Is it possible through some trick like changing blade angle or reverse the prob rotation direction? It would have been hard for piloting, but is this theoretically possible?
Wings generally only produce enough lift to keep an aircraft aloft when air is flowing over them in their intended direction. If you reverse the airflow over the wing (by moving backwards in the air, for example) the wing would no longer be producing the necessary lift, and the aircraft would "descend at an extremely rapid rate" until a normal airflow over the wings was restored. (That's the polite way of saying "the darn thing falls out of the sky like a rock!")
Move? Yes. At least on the ground.
This has been demonstrated on more than one occasion by Fat Albert, the C-130 that supports the Blue Angels. While the propellers themselves do not reverse, the blade pitch is changed to produce reverse thrust (slowing the aircraft the same way thrust reversers do on a jet engine, and in this case reversing its direction of travel).
Note that there is one notable exception to the "airplanes can't fly backwards" rule, which the article Ethan linked to alludes to: If the wind velocity exceeds the aircraft's stall speed it's possible for an aircraft to "fly" at its minimum airspeed, but be moving backwards relative to the ground.
This is a bit of a cheat though: The airplane still thinks it's flying forward (the relative velocity of the wind over the wings is in the "normal" direction, and the airspeed is fast enough to create enough lift to sustain flight). It just happens the the airspeed includes a headwind component sufficient to give the aircraft a net "negative" groundspeed.
The hypothetical P-51 in your question would require sustained winds of about 83 knots to make this trick work (we generally call that a hurricane), but something like a Piper Cub can do it at much more reasonable wind speeds.
In short, no.
First, the wing of an aircraft is designed to produce lift in only one direction. Airflow moving backwards over the airfoil would not be directed around it properly; the air coming across what's supposed to be the trailing edge would be divided too cleanly (so it could stall too easily) and wouldn't be accelerated as quickly by the gentler slope on what's supposed to be the back side of the wing, thus reducing lift. The leading edge, now the trailing edge, would increase drag and further reduce lift as the boundary layer would separate too soon along its curve. In other words, a wing moving backward produces very little lift and much more drag, both bad for an airplane trying to stay in the air.
In addition, most propeller-driven aircraft have their wing chords angled slightly upward from the thrust vector of the engine, which provides a nonzero angle of attack in level flight. This provides more lift at the cost of slightly higher drag, and allows a plane to maintain altitude more easily at cruising speeds with the nose level. In reverse "flight", this would end up a negative angle of attack, reducing lift even further.
Lastly, the horizontal stabilizer is designed to provide downforce in forward flight to counteract a slightly forward center of gravity (this basic design causes desirable stall behavior, causing the plane to nose down to restore normal airflow). This is accomplished in low wings with a slight downward angle of the horizontal stabilizer (or a slight up-angle to canards), and in high-wings by using the downwash from the wing to push on the tail. Moving backward, there's no downwash to balance the weight at the nose, and a downward cant would actively push the tail up as the wind moved past it, in either case flipping the plane into a nose-down attitude (also a desirable recovery behavior if you find yourself hanging by your prop).
In a stellar engineering choice by aircraft designers, they orient the curve of the wings and trim the horizontal stabilizers to produce lift and balancing trim force when the aircraft is moving in the direction its occupant(s) would call "forward", i.e. the direction the pilot's seat is facing.
There are a few aircraft, notably late Soviet designs like the MiG-29 and Su-27, that were engineered for desirable "post-stall" behavior. These aircraft are capable of remaining stable and controllable in extreme angles of attack (exceeding 90° off-chord) and are the best examples of an aircraft that can "fly backward", at least for a couple of seconds. The maneuvers involved include the tailslide (pull in to the vertical, stall nose-up, and fall back to earth tail-first, then pull back on the stick to kick your tail out behind you and drop the nose to recover) and the cobra (from full throttle, cut the engine and pitch up hard to intentionally stall the aircraft and rotate nose-up, then center the stick to allow the plane to nose-down). Most counterpart U.S. aircraft are incapable of these maneuvers as they're engineered to avoid stalling, following the "energy management" theory of Western combat maneuvering (where stalling, regardless of airspeed, means you're out of energy to maneuver, as you either have insufficient forward airspeed to maintain your turn, or you've just turned your plane's wings into air brakes).
When, as a youngster, I made model planes, I tried this. The result is very unstable and usually the tail lifts on launch causing the aircraft to flip over. I think that, with the use of computer control to counteract the inherent instability and a specially made propeller it might be possible but the development time and expense means that no-one would ever try to do it..
The problem is that the tail assembly of a standard configuration acts like a weather vane. It naturally wants to turn away from the direction of airflow.
In theory, yes, inefficient, very very unstable, with the control surfaces facing the airflow rather than behind it so a big risk of the airflow snatching the controls and forcing them over to full travel - with very bad results. The aeroplane would want to flick round and fly in the opposite direction because of the way its designed to fly forwards.
There is a relation between the thrust provided by the engine and the lift created by the profile of the wings. Usually this relation is not the same backwards, so it will not fly backwards.
Propeller planes like the P-51 has an asymmetric aerodynamic profile that cannot provide the same lift moving backwards.
There is some aerodynamic profiles that are near to be symmetric, but requires a power plant much greater than a propeller. Usually this power plant cannot provide the same thrust backwards than forward.
If reverse thrust was generated (you couldn't do this simply by reversing the prop) then a plane could fly backwards.
While the wings are shaped to generate lift as they pass through the air in the forward direction, by using angle of attack and enough thrust you can generate lift in any direction. Angle of attack changes the apparent profile of the wing. The same principle allows planes to fly upside down or sideways in knife edge. The simplest example is how a paper plane can still glide with completely flat wings.
Try riding your bicycle backwards down a steep hill if you are not sure what other writers here mean by passive pitch stability and yaw stability.
The reason why the big tail and elevators are well behind the middle of the wings is to make sure that when flying forward, they will tend to straighten any wobble.
Go to the pub and have a look at how darts fly if you want. You can try throwing one of those backwards too.
You don't need reverse thrust to do this. Just pull the nose way up, and let the speed bleed off until your vertical speed is zero. Then you tailslide. Most planes are designed to make this not very easy to do, but if you move the CG far enough back, by putting bricks in the tail, you can do it.
The trouble with that is, unless your plane is specially made, and you are specially trained, you will have a very difficult time not just sliding all the way to the ground (and voiding the warranty).