How to refresh a ASPxGridView summary value on the client side

The ASPxGridView is a server side control, so it renders on the server side.

If you know how the summary value should be changed using the client side code, you need to do the following:

1) add the ASPxLabel to the column's FooterTemplate container and set its ClientInstanceName to a some value, for example, lblFooter;
2) use the lblFooter.SetText('some text') to change the displayed summary value.

Here is some sample code:

[ASPx]

<dx:GridViewDataTextColumn FieldName="CategoryID" ReadOnly="True" VisibleIndex="1">
<EditFormSettings Visible="False" />
<FooterTemplate>
<dx:ASPxLabel ID="ASPxLabel1" ClientInstanceName ="lblFooter" runat="server"
Text="<%# GetSummaryValue(Container)%>">
</dx:ASPxLabel>
</FooterTemplate>
</dx:GridViewDataTextColumn>
....

[C#]

protected string GetSummaryValue(GridViewFooterCellTemplateContainer container) {
ASPxGridView gridView = container.Grid;
GridViewDataColumn column = container.Column as GridViewDataColumn;
if(column == null)
return string.Empty;
for(int i = 0; i < gridView.TotalSummary.Count; i ++)
if(gridView.TotalSummary[i].FieldName == column.FieldName) {
return gridView.GetTotalSummaryValue(gridView.TotalSummary[i]).ToString();
}
return string.Empty;
}

Dynamically add controls to footer row using RowTemplate

Create a Class that inherits ITemplate and add controls the container ; you want to add.
Assign the object of that class to ASPxGridView's Templates.FooterRow property as:

ASPxGridView1.Templates.FooterRow = new CustomFooterRowTemplate();
And the code snippet of the template class is below:
public class CustomFooterRowTemplate: ITemplate
{            
     void ITemplate.InstantiateIn(Control container)
     {
         Button button = new Button();
         button.Text = "Test"; 
         container.Controls.Add(button);
     }
}

have an idea from this and you can add more controls and even you can use their event handler in the custom template except using on the RowCommand event.