Best Answer - Chosen by Voting
This first one is fine. It could be 'life' or 'lives'. Life would focus more on an individual case and lives more groups of people.
For the second sentence, it is correct but I'm not sure if it means what you think it does. The way it is written, it means that the reason people should be respected is because of their private life. I think you meant that people should respect others' private life.
If that's what you meant, this might be better:
Everyone has the right to have their private life respected.