1. Why do we need automated tests when we can test manually?
  2. Isn't that just waste of time/money?
  3. We could add more features instead.

Mostly for the regression but in some cases it is very hard or impossible to test manually. Writing tests can be a huge expense. Running tests the 2nd time is where you start to see the benefit. After 10 or 100 times you'll really see the profit.