setState is async, and you need to invoke the function in the callback.

this.setState({
  languages: [...langs]
}, () => console.log(this.state.languages)
);

Many ways to do it, really. Here's one:

this.setState(prevState => (
  {appointmentsData: {...prevState.appointmentsData}, newAppt}
));

Though your approach should work too, if you just add the appointmentsData: first. Like so:

this.setState({appointmentsData: {...this.state.appointmentsData, ...newAppt}});

This will spread all the previous values into a new object, plus the one you want to add.

I personally always use the functional way of setting the state when the new one depends on a previous state value, but your way is fine here too.

Simply assign the property and it will overwrite the old one.

export default function(state = initialState, action) {
  switch (action.type) {
    case GET_BOOKS:
      console.log(action.payload.results);
      // spread current state and inaddition to that set new books data
      // which overwrites books property from old state
      return { ...state, books : action.payload.results };
      // spread --^^^^^^^^^^^^^^^^^^^^^^^^^^^---
    default:
      return state;
  }
}

UPDATE : If you want to concatenate it with existing then do something like this.

export default function(state = initialState, action) {
  switch (action.type) {
    case GET_BOOKS:
      console.log(action.payload.results);
      return { ...state, books : [...state.books, ...action.payload.results] };
    default:
      return state;
  }
}

FYI : The ...state part is for copying other state properties(assumes there exists other state values)