You need to assign FullModeItemTemplate
for that to work:
<toolkit:ListPicker x:Name="sightingTypesPicker" ItemsSource="{Binding sightingTypes, ElementName=this}">
<toolkit:ListPicker.ItemTemplate>
<DataTemplate>
<StackPanel>
<TextBlock Text="{Binding Name}" FontSize="{StaticResource PhoneFontSizeSmall}"/>
</StackPanel>
</DataTemplate>
</toolkit:ListPicker.ItemTemplate>
<toolkit:ListPicker.FullModeItemTemplate>
<DataTemplate>
<StackPanel>
<TextBlock Text="{Binding Name}" FontSize="{StaticResource PhoneFontSizeSmall}"/>
<TextBlock Text="{Binding SomeOtherProp}" FontSize="{StaticResource PhoneFontSizeSmall}"/>
</StackPanel>
</DataTemplate>
</toolkit:ListPicker.FullModeItemTemplate>
</toolkit:ListPicker>
EDIT: To answer your question B: You can use the SelectedItem DependencyProperty to get the instance of the selected object:
With MVVM approach:
<toolkit:ListPicker x:Name="sightingTypesPicker"
ItemsSource="{Binding SightingTypes}"
SelectedItem="{Binding SelectedSigntingType, Mode=TwoWay}">
With code-behind approach:
sightingTypesPicker.SelectionChanged += (s, e) => {
MessageBox.Show(((SightingType)e.AddedItems[0]).ID);
};