: Does gravity travel instantanious, or does it travel at a certain speed. And can you detect what is inside a black hole, or at least the mass distribution, by measuring the gravity of the hole? What if you drop something into the hole and measures its position by the use of its gravity? what will then be detected? That the object has the same position as is given by the light emitted by the object and the object being "freezed" on the event horizon, or will something else be detected, for instance the objects position inside the event horizon.

: If gravity travels with a finite speed, can there exist a gravity field so strong, that gravity can't escape, and what happens then?

Gravity travels at the speed of light. The mass distribution of a black hole cannot be ascertained, only its total mass. As the next comment of yours indicates, to an outside observer, the object is never seen to fall in, i.e. it appears to freeze at the event horizon. The simple answer to your last question is that the gravity field around a black hole is also frozen, and therefore remains in place.