I have some questions regarding Einsteins theory of Relativity that should be fairly easy to answer. Lets say we make an experiment where we have a rocket (with an astronaut inside) that travels very close to the speed of light and it is heading away from Earth. Also back on earth I have an observer that makes measurements regarding the rocket that travels very close to the speed of light.

Question 1: What is the speed of the rocket that the earth observer would measure?

Lets change the above experiment and place the rocket very close to the event horizon of a black hole. According to what I have heard and read the rocket would seem to stand still as our observer see it back on earth.

Question 2: What is the speed that the earth observer would make about the rocket in this situation?

Question 3: Are the two experiments the same or are they somehow fundamentally different? Would an object seem standing still while traveling very close to the speed of light?