If you wish to maintain the order of the string in the list, you could try adding the item as shown in the provided WebCombo sample AddUnboundRow.aspx.

The attached sample bin project folder is not using the latest WebUI R2 2009 release, I have taken the liberty in using the latest dll to test the issue.

#1 In which event handler / function do you wish to use the GetClientAction()? I did not see any usage of the GetClientAction in the attached project.

#2 and #3 Analyzing the OnForwardNavigation and OnBackNavigation event handler, it seems the error is caused by SetCalendarDate() function. In your configuration, you will not need to use the SetSelectedDate() function the SetSelectedDate property already suffice for navigating. Here is the modified event handler:

function DoForwardNavi(ControlID, ViewType, CurrentDate, PeriodStarDate, PeriodEndDate)
{
    var WbSchdlr = ISGetObject("wbSchdlr");
    WbSchdlr.AddInput("year", PeriodStarDate.getFullYear().toString());
    WbSchdlr.AddInput("month", (PeriodStarDate.getMonth() + 1).toString());
    WbSchdlr.AddInput("day", PeriodStarDate.getDate().toString());
    
    WbSchdlr.ViewSettings.SelectedDate = PeriodStarDate;
    WbSchdlr.RefreshAll();
    
    return false;
    
}

Unfortunately, we could not change the height of the caption area during export. However my test show that the available height is sufficient for 2 line of caption. For example, if we set the caption to: 

e.Table.Caption = "New Table Caption Line 1\r\nNew Table Caption Line 2\r\nNew Table Caption Line 3\r\nNew Table Caption Line 4";

The shown caption will be 

New Table Caption Line 1
New Table Caption Line 2

At the center of the exported PDF report.

You could modify the connection string programatically during ISDataSource object created server side event using reflection. However the DB you changed to must have the same structure with the one you assign in the design mode. Here is the snippet of object created server side event handler:

protected void ISDataSource1_ObjectCreated(object sender, ISNet.WebUI.DataSource.ISDataSourceEventArgs e)
{
    OleDbConnection conn =
       (OleDbConnection)e.ObjectInstance.GetType().GetProperty("Connection", BindingFlags.NonPublic | BindingFlags.Instance).GetValue(e.ObjectInstance, null);
    conn.ConnectionString = "Provider=Microsoft.Jet.OLEDB.4.0;Data Source=|DataDirectory|\\WebScheduler_Software_2.mdb;Persist Security Info=True";
}

The original data source of the ISDS in the snippet is WebScheduler_Software.mdb

I tried to replicate the issue in the Timeline month view in ViewMode_Timeline_Month.aspx provided WebScheduler sample. The event has refresh successfully when we change month and hide certain resources without the need to click on the "Refresh View".

Please make sure you already have the latest WebScheduler 3 and WebUIFramework 3 build which is build 2 and build 750 respectively.