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The results showed that Ötzi died over 5000 years ago, sometime between 33 BC. Uranium has a very long half-life and so by measuring how much uranium is left in a rock its approximate age can be worked out.
By measuring the amount of carbon-14 left in dead organic material the approximate time since it died can be worked out.
Radiocarbon decays slowly in a living organism, and the amount lost is continually replenished as long as the organism takes in air or food.
Once the organism dies, however, it ceases to absorb carbon-14, so that the amount of the radiocarbon in its tissues steadily decreases.
Using the decays of uranium and thorium, our galaxy has been found to be between 10 and 20 billion years old and the earth has been found to be 4.6 billion years old. Within experimental error, this estimate agrees with the 15 billion year estimate of the age of the Universe.
The answers to these questions can be found in this lesson on the applications of nuclear chemistry.