Is it possible to change user’s password with the okta angular widget, or do I have to create one myself and use the api?
If you use the Sign-In Widget, yes. See https://github.com/okta/samples-js-angular/tree/master/custom-login for an example.
I saw that the forgot password is on Sign-In Widget. But, I do not understand how actually Sign-In Widget can help with change password. Can you please clarify it?
So, there is no flow for change password, where the user can enter the old password and the new password, the password is changed only with recovery flow on sign-in widget ?
Yes, that is correct.