1. Which of Einsteins theories of relativity, the Special or the General one, was confirmed/accepted quicker? What was the experiment Eddington did and what did it confirm?
This is somewhat arguable, but Special relativity was accepted by some important names who used it in their research within a couple of years of it being published. General relativity was accepted 4 years after being published, when Eddington confirmed Einstein's prediction that the Sun would gravitationally bend the light of stars behind it. Eddington confirmed this during a solar eclipse in 1919.
2.In which connection did Einstein make the statemnt "God does not play dice". What did he mean with that?
Einstein was unhappy with quantum mechanics because it is based on probability. He firmly believed that a scientific theory shouldn't have this type of uncertainty involved.
3. What was Einstein's biggest frustration in later life in terms of scientific goals he wanted to achieve?
Einstein's greatest frustration was that he was unable to unify all of the forces into a unified field theory. So far, this has yet to be done.
4. For which work did he get the Nobel prize in physics? Try to explain what this discovery refers to.
Einstein received the Nobel Prize in 1921 for his work on the Photoelectric Effect. This work showed that light is quantized (it has a particle nature). This was shown by colliding electrons with a metal plate, which then ejected photons.
5. Considering Einstein's life and education, would he have been able to achieve similar success following such a somewhat unusual career path in the current time and society?
If you are unfamiliar with Einstein's life and would like to know more, I highly recommend the book "Einstein: His Life and Universe" by Walter Isaacson. My personal opinion is that Einstein probably could have made the same discoveries, but due to the way society and the scientific community work today, he probably would have taken a much longer time to convince people of his ideas.