Yes, humanity can clone extinct animals, so long as they have gone extinct in the recent past. DNA can survive for a few hundred years, so as long as the animal went extinct during that time and a good source of DNA can be found, cloning that animal can occur.
Sure, maybe in the distant future science may be able to clone an extinct animal. It is true DNA lasts a long time, even longer than a million years if it is fossilized. So right now science can't clone extinct animals but it may well be possible in the near future.
No, humans cannot close extinct animals, because the scientific knowledge that would allow scientists to close extinct animals is not developed enough to make that happen. To clone something, there need to be live cells to work from. Scientists do not have the know-how to clone something that has already died.