Accidentally deleted all indices from the cluster. How do I restore the data?

This is not correct. I don't know what issue you ran into, but internal services do not use the elastic user.

[2018-09-17T12:30:10,755][INFO ][o.e.x.s.a.AuthenticationService] Authentication of [elastic] was terminated by realm [reserved] - failed to authenticate user [elastic]

This is not an error. It is an informational message that the incorrect password was provided for te elastic user, but it does not prevent the service from starting.