What are examples of designs that mitigate the issues of driving in heavy rain?
The best mitigation is not to drive in it. Most roads are designed with a crown in the road (high spot in the middle), which allows the water to run off at a fairly rapid clip. This helps eliminate standing water to an extent. During extreme rain, this isn't possible and you will run into it from time to time.
The best example of mitigation would be tire tread design. There are three basic tread designs: Symmetric, asymmetric, directional
The asymmetric tire is designed for the best of both worlds. One half of the tire is for dry performance, while the other side is for wet performance as it pumps the water away from the tire. Mind you, both sides work in both situations, it's just that each side does its own job better than the other.
Some vehicles (4x4's with the proper setup) have what is called a snorkeling kit, which basically puts the air intake and exhaust pipes above the roof line of the vehicle:
This allows the vehicle to traverse water up to the point of where the intake is at. If it goes deeper, it too will suck up water. Please note, this should only be used in standing or very slow moving water. As was stated, if you go into fast moving water, it will move the vehicle and it will be swept down steam.
Will the water gets inside the air intake pipe?
Will it get inside the engine?
What happens if the engine is flooded with water?
It can get inside the air intake pipe if the intake is low enough and the water high enough. When this happens, if the engine is running, it will suck it up into the intake, right after which will head directly into a cylinder or two. When this happens, the engine will stop as the intake valve closes and the piston starts to head upward. Normally at this point, the air/fuel mixture is being compressed. Since water will not compress, the engine stops dead in its tracks. This is called hydrolock (aka: hydrostatic lock).
Is there any way to recover from this situation?
In severe cases, deformation of mechanical parts can occur, which would at the worst, require a complete engine replacement. This usually depends on engine speed at the time of water ingest. If it's at idle speed, the engine probably won't suffer too much ill effects. It really depends on how long and how far the engine is submerged ... if completely submerged for days, the entire car is most likely going to be shot. If you get to it quickly and the only water in the engine is what was sucked up through the intake, it will probably survive.
If the engine is not physically damaged during the hydrolock process, it takes a little bit to get the engine going again. You would need to remove the spark plugs and rotate the engine, allowing the water to come up out of the hole and/or evacuate down the exhaust pipe after enough revolutions of the engine has occurred. You'd probably want to do this by hand. You'd also need to suck any fluid out of the cylinder which might remain. Next, you'd need to change the oil and filter, as more than likely, some of the water has seeped into the crank case around the piston rings. The only way you'd really know if there was internal damage (if it didn't physically manifest it self, like a rod through the block) would either be through getting all of this done. Through the process of turning the engine over after the spark plugs are removed, if you notice any turning issues, there is probably something mechanical which is bad. With the spark plugs out, the engine should turn over fairly easily. There is some resistance due to cam shaft friction, but other than that, it shouldn't be an issue. You would then try to running the engine. If it runs good, it's in good shape. If it doesn't, you have issues. You could tear the engine down to see, as well, but that is probably overkill at this point, especially if there aren't any issues with it.