A few questions on IDataErrorInfo Interface

I've looked at a few examples of implementing the IDataErrorInfo interface and all of those implemented that somewhat like this:

public string Error => null;
public string this[string columnName] {
    get {
        string res = null;
        switch (columnName) {
            case "FirstName":
                if (FirstName != "test") res = "First Name Invalid!";
                break;
            case "LastName":
                if (LastName != "test") res = "Last Name Invalid!";
                break;
        }
        return res;
    }
}

What's the purpose of public string Error and how to use that instead of returning null? In xaml some of those examples used a predefined style targeting TextBox and others used a Label or ToolTip like these:

<TextBox x:Name="Fname" 
         Text="{Binding FirstName, UpdateSourceTrigger=PropertyChanged, ValidatesOnDataErrors=True}" 
         ToolTip="{Binding ElementName=Fname, Path=(Validation.Errors)[0].ErrorContent}" />

<Label Content="{Binding ElementName=Fname, Path=(Validation.Errors).CurrentItem.ErrorContent}"/>

Can I avoid x:Name="Fname" and ElementName=Fname when it's used as a ToolTip and shorten the expression (Validation.Errors)[0].ErrorContent?

---

EDIT

Probably DataAnnotations is the most elegant way to to validate individual property as well as the whole model/viewmodel along with these:

public string Error => null;
public string this[string columnName] {
    get {
        var validationResults = new List<ValidationResult>();
        if (Validator.TryValidateProperty(
            GetType().GetProperty(columnName).GetValue(this), 
            new ValidationContext(this) { MemberName = columnName }, 
            validationResults
            )) return null;

        return validationResults.First().ErrorMessage;
    }
}

To validate the whole model I just am supposed to call:

Validator.TryValidateObject(this, new ValidationContext(this), null, true);

in CanExecute of ICommand. This example also didn't use the public string Error.

The Error property is ignored by the WPF binding engine so you only have to care about to implement the indexer.

By the way, it's recommended to implement and use the INotifyDataErrorInfo interface instead of IDataErrorInfo since .NET Framework 4.5.