Since nothing can travel faster than the speed of light, nothing can escape from inside the event horizon. Here in the outside universe, we have no information whatsoever about what is going on inside an event horizon. However, we have no way of confirming this prediction by observation. If the dense core, once it is compressed within the event horizon, suddenly turns into a flock of enormous cosmic flamingoes, we simply would have no way of knowing. Information cannot travel from inside an event horizon to outside an event horizon.
Black holes are much more benign than that.
The Earth's orbit would remain unchanged. The gravitational attraction between the Earth and Sun will be the same as long as the masses and distances remain constant. It doesn't matter whether the Sun is a black hole or a sphere of hydrogen and helium or a lump of peanut butter, as long as the mass is the same. Black holes are inescapable only if you venture inside the event horizon. The event horizon of a black hole which forms from a collapsing star is quite small - only 10 miles or so in radius.