1) Try setting grid.ListBoxSelectionMode = SelectionMode.MultiSelect. This should allow your user to use the keyboard and mouse to select multiple rows. I am not sure what you mean by selecting rows with your context menu. Are you going to have a menu iten that says "Select rows 1-3"? If so, you can use grid.Selections.Add(GridRangeInfo.Rows(1,3)) to do this.
2) One way you can do this is to use SendKeys and forward a Delete key onto the grid from your button handler.
private void button1_Click(object sender, System.EventArgs e)
{
this.gridDataBoundGrid1.Focus();
SendKeys.Send("{DELETE}");
}
One comment is that the grid only deletes the active range. If you have several disjoint selections, the grid by default only deletes the active one. If you want to delete all on them, then you can try the technique in this KB.
http://www.syncfusion.com/Support/article.aspx?id=10443
