Wpf – Merge header columns datagrid wpf

In your DataGridTemplateColumn you have SortMemberPath set to "". If you set this to an actual property on the item (say, CompleteDate), you should be able to sort. You can also set CanUserSort="true" or CanUserSort="false" on selected columns.

SortMemberPath gives the property to sort on when the user attempts a sort. If this isn't set, then the grid doesn't know how to sort that column ( it does not use the text in the column)

            <my:DataGridTemplateColumn  SortMemberPath="CompleteDate" Header="Complete Date" CanUserSort="true">
            <my:DataGridTemplateColumn.CellTemplate >
                    <DataTemplate>
                        <TextBlock>
                            <TextBlock.Text>
                                <Binding Path="CompleteDate" ConverterCulture="en-GB" StringFormat="{}{0:MM/dd/yyyy}"/>
                            </TextBlock.Text>
                        </TextBlock>
                    </DataTemplate>
                </my:DataGridTemplateColumn.CellTemplate>
            </my:DataGridTemplateColumn>

For single click DataGrid checkbox you can just put regular checkbox control inside DataGridTemplateColumn and set UpdateSourceTrigger=PropertyChanged.

<DataGridTemplateColumn.CellTemplate>
    <DataTemplate>
        <CheckBox IsChecked="{Binding Path=IsSelected, UpdateSourceTrigger=PropertyChanged}" />
    </DataTemplate>
</DataGridTemplateColumn.CellTemplate>