I have created a sample in order to replicate the issue, however using the latest build of WebGrid and WebUI Framework, I could not replicate the issue.

Attached is the simple sample I created to test the scenario.

The sample is using northwind.mdb, in order to simulate the multi row data I inserted <br/> tag in Notes column after . 

WebScheduler has a javascript function to move to a selected date. Here is the snippet to move to a week from the currently selected date:

function MoveSchedulerByCalendar() {
    var sched = ISGetObject("WebScheduler1");
    sched.Calendar.MoveDayBy(7);
    sched.RefreshAll(true);
}
function MoveSchedulerBySelectedDate() {
    var sched = ISGetObject("WebScheduler1");
    
    var currentDate = sched.ViewSettings.SelectedDate;
    currentDate.setDate(currentDate.getDate() + 7);
    sched.RefreshAll(true);
}

The first snippet will be applicable if the Calendar object is loaded, if the Calendar is not loaded you could use the second snippet. 

Regarding the lack of documentation for WebScheduler, I will inform this to our documentation team for consideration. 

The behavior is by design, during DayEvents-OnClick the selected value has not been applied to the WebInput. In order to determine the WebInput that triggered the event and the currently selected date, you could use the event parameter. Here is the snippet:

function UpdateDates(ctrlId, selectedDay, selectedMonth, selectedYear) 
{
    var currentInput = ISGetObject(ctrlId);
    
    var dataCaptureDate = ISGetObject("wiCaptureDate");
    var webInput1 = ISGetObject("WebInput1");
    var webInput2 = ISGetObject("WebInput2");
    var strMessage = "";
    var selectedDate = new Date();
    selectedDate.setFullYear(selectedYear, selectedMonth - 1, selectedDay);
    strMessage += "Current input:" + selectedDate.toDateString() + "\r\n";   
    if (ctrlId != "wiCaptureDate")
        strMessage += "Data Capture Date:" + dataCaptureDate.GetValueData() + "\r\n";
    if (ctrlId != "WebInput1")
        strMessage += "Web Input1:" + webInput1.GetValueData() + "\r\n";
    if (ctrlId != "WebInput2")
        strMessage += "Web Input2:" + webInput2.GetValueData() + "\r\n";
    alert(strMessage);
}

The text file issue occurs because there is a , character in the Address column while we are using ,  as a column separator. In order to remedy this issue you could enclosed the Address data in a " "  during Export server side event in order to set the data as a single column data. Here is the snippet:

protected void WebGrid1_Export(object sender, ISNet.WebUI.WebGrid.ExportEventArgs e){
    foreach (WebGridRow wgRow in e.Table.Rows)
    {
        wgRow.Cells.GetNamedItem("Address").Value = "\"" + wgRow.Cells.GetNamedItem("Address").Value + "\"";
        wgRow.Cells.GetNamedItem("Address").Text = "\"" + wgRow.Cells.GetNamedItem("Address").Text + "\"";
    }
}