Do laws of physics apply below the event horizon? It appears as if black holes had such gravity as to have an escape velocity higher than c, which means that things are pulled inwards at higher speeds than the speed of light. Or am I overlooking something?
The event horizon of a non-rotating black hole is the place where the escape velocity is
exactly the speed of light... not faster then.
From the POV of a distant observer, if nothing else happened, it would take an infalling mass an infinite amount of time to reach the event horizon... but that is not all that happens.
Oversimplifying a bit,
The Schwarzschild radius (the radius of the event horizon) depends on the mass.
If the total mass is inside this radius, then the object is a black hole with this radius.
If not all the mass is inside this radius, then the object is a star or planet or something.
There is no way anyone outside that radius can know what is going on inside it, once a black hole has formed.
You can have a black hole mass M, with mass m falling towards it.
The radius for M+m is bigger than for M alone.
When m gets close enough that it is inside the M+m radius: the black hole gobbles it.
This happens before it reaches the event horizon... so never gets to the speed of light.