What I would like is to be able to export to a named sheet and keep the other sheets in file. For example:
"Sheet 1" (with new values), "Sheet2" (with old values)

Using your current naming convention, the Option might be named FileExportMode.CreateOrOverrideSheet

When using Crystal or CrystalDark themes, the resize cursor is not showing to widen/shrink the columns:

Expected:

Actual:

My pivot grid data size is 90,388 rows, and I export data to xlsx format with SheetName = "data".

The output file generated in this case (correctly) has 65536 rows on sheet "data" and the remaining 24852 rows on the sheet "data_2" (since SheetMaxRows = 65536 and total rows > SheetMaxRows, second sheet "data_2" is added automatically).

But the rows on the sheet "data_2" are written starting from line number 65538. The data on sheet "data_2" starts on line 65538 and goes till line 90389.

Expected:

Actual:

Workaround; use the following custom renderer:

        public class MyRenderer : SpreadExportRenderer
        {
            public override void CreateCellSelection(int rowIndex, int columnIndex)
            {
                if (rowIndex > (int)Telerik.WinControls.UI.Export.ExcelMaxRows._65536)
                {
                    rowIndex = rowIndex % (int)Telerik.WinControls.UI.Export.ExcelMaxRows._65536 - 1;
                }
                else
                {
                    rowIndex = rowIndex % (int)Telerik.WinControls.UI.Export.ExcelMaxRows._65536;
                }
                base.CreateCellSelection(rowIndex, columnIndex);
            }
        }

Here is my code for localizing the Sum aggregate function. The obtained result is a partial translation:

        public RadForm1()
        {
            PivotGridLocalizationProvider.CurrentProvider = new MyEnglishPivotGridLoclizationProvider();
            InitializeComponent();
        }

        private void RadForm1_Load(object sender, EventArgs e)
        {
            this.ordersTableAdapter.Fill(this.nwindDataSet.Orders);

            this.radPivotGrid1.RowGroupDescriptions.Add(new DateTimeGroupDescription() { PropertyName = "OrderDate", Step = DateTimeStep.Year, GroupComparer = new GroupNameComparer() });
            this.radPivotGrid1.RowGroupDescriptions.Add(new DateTimeGroupDescription() { PropertyName = "OrderDate", Step = DateTimeStep.Quarter, GroupComparer = new GroupNameComparer() });
            this.radPivotGrid1.RowGroupDescriptions.Add(new DateTimeGroupDescription() { PropertyName = "OrderDate", Step = DateTimeStep.Month, GroupComparer = new GroupNameComparer() });
            this.radPivotGrid1.ColumnGroupDescriptions.Add(new PropertyGroupDescription() { PropertyName = "EmployeeID", GroupComparer = new GrandTotalComparer() });
            this.radPivotGrid1.AggregateDescriptions.Add(new PropertyAggregateDescription() { PropertyName = "Freight", AggregateFunction = AggregateFunctions.Sum });
            this.radPivotGrid1.AggregateDescriptions.Add(new PropertyAggregateDescription() { PropertyName = "Freight", AggregateFunction = AggregateFunctions.Count });
            this.radPivotGrid1.FilterDescriptions.Add(new PropertyFilterDescription() { PropertyName = "ShipCountry", CustomName = "Country" });
            this.radPivotGrid1.DataSource = this.ordersBindingSource;
        }

        class MyEnglishPivotGridLoclizationProvider : PivotGridLocalizationProvider
        {
            public override string GetLocalizedString(string id)
            {
                switch (id)
                {
                    case PivotStringId.Sum:
                        return "Soma"; 
                    default:
                        return base.GetLocalizedString(id);
                }
            }
        }

The error is reproducible in the First look example of RadPivotGrid:

Check the attached screenshot:

How to reproduce: see the attached video

Workaround:
public partial class Form2 : Form
{
    public Form2()
    {
        InitializeComponent();

        this.radPivotFieldList1.DragDropService = new CustomPivotFieldListDragDropService(this.radPivotFieldList1);
    }

    private void Form2_Load(object sender, EventArgs e)
    {
        // TODO: This line of code loads data into the 'nwindDataSet.Orders' table. You can move, or remove it, as needed.
        this.ordersTableAdapter.Fill(this.nwindDataSet.Orders);

    }
}

public class CustomPivotFieldListDragDropService : PivotFieldListDragDropService
{
    private RadPivotFieldList fieldList;
    private Telerik.WinControls.UI.PivotFieldList.FieldPayload payload;

    public CustomPivotFieldListDragDropService(RadPivotFieldList fieldList)
        : base(fieldList)
    {
        this.fieldList = fieldList;
    }

    protected override void PerformStart()
    {
        base.PerformStart();

        Telerik.WinControls.UI.PivotFieldList.IField draggedField = this.GetField(this.Context);

        if (draggedField == null)
        {
            this.Stop(false);
            return;
        }

        this.payload = new Telerik.WinControls.UI.PivotFieldList.FieldPayload(draggedField);
    }

    protected override void OnPreviewDragOver(RadDragOverEventArgs e)
    {
        RadElement targetElement = this.DropTarget as RadElement;
        Telerik.WinControls.UI.PivotFieldList.IField targetField = this.GetField(targetElement);

        if (targetElement != null && targetElement.ElementTree.Control == this.fieldList.ReportFiltersControl && this.payload != null)
        {
            foreach (Telerik.WinControls.UI.PivotFieldList.IField field in this.fieldList.ViewModel.Filters)
            {
                if (field.FieldInfo == payload.DraggedField.FieldInfo &&  this.Context is TreeNodeElement ))
                {
                    e.CanDrop = false;
                    this.payload.SetDestination(null);
                    this.payload.RemoveFromSource = false;

                    return;
                }
            }
        }

        base.OnPreviewDragOver(e);
    }

    private Telerik.WinControls.UI.PivotFieldList.IField GetField(object context)
    {
        RadListVisualItem listItem = context as RadListVisualItem;
        TreeNodeElement treeItem = context as TreeNodeElement;
        PivotFieldListItemButton button = context as PivotFieldListItemButton;

        if (button != null)
        {
            listItem = button.Owner;
        }

        Telerik.WinControls.UI.PivotFieldList.IField field1 = null, field2 = null;
        if (listItem != null && listItem.Data != null)
        {
            field1 = listItem.Data.DataBoundItem as Telerik.WinControls.UI.PivotFieldList.IField;
        }

        if (treeItem != null && treeItem.Data != null)
        {
            field2 = treeItem.Data.DataBoundItem as Telerik.WinControls.UI.PivotFieldList.IField;
        }

        return field1 ?? field2;
    }
}

How to reproduce: 
Me.RadPivotGrid1.DataSource = Nothing

Workaround: 
DirectCast(Me.RadPivotGrid1.DataProvider, LocalDataSourceProvider).ItemsSource = Nothing
Dim viewModel = Me.RadPivotGrid1.PivotGridElement.GetType().GetField("viewModel", BindingFlags.Instance Or BindingFlags.NonPublic).GetValue(Me.RadPivotGrid1.PivotGridElement)
viewModel.GetType().GetProperty("DataProvider").SetValue(viewModel, Nothing)

The issue may manifest if aggregate descriptions are added on the pivot`s column axis and if their member does not return data.

How to reproduce: check the attached project and screenshots, the correct items are shown in screenshot correct-items-calculated-field.jpg

Workaround: 
public partial class Form1 : Form
{
    private LocalDataSourceProvider provider;

    public Form1()
    {
        InitializeComponent();

        //Setup pivot and add calculated field

        //Workaround
        this.radPivotFieldList1.ValuesControl.CreatingVisualListItem += ValuesControl_CreatingVisualListItem;
    }

    private void ValuesControl_CreatingVisualListItem(object sender, CreatingVisualListItemEventArgs args)
    {
        args.VisualItem = new MyPivotFieldListVisualItem(this.radPivotFieldList1.ViewModel);
    }
}

public class MyPivotFieldListVisualItem : PivotFieldListVisualItem
{
    FieldListViewModel viewModel;

    public MyPivotFieldListVisualItem(FieldListViewModel viewModel)
        : base(viewModel)
    {
        this.viewModel = viewModel;
    }

    protected override void UpdateContextMenu()
    {
        base.UpdateContextMenu();

        PivotFieldListItemButton button = (PivotFieldListItemButton)typeof(PivotFieldListVisualItem).GetField("button", System.Reflection.BindingFlags.Instance | System.Reflection.BindingFlags.NonPublic).GetValue(this);
        string providerName = this.viewModel.DataProvider != null ? this.viewModel.DataProvider.GetType().FullName : String.Empty;
        if (this.Data == null)
        {
            return;
        }

        if (this.Data.DataBoundItem is Value && !(providerName.Contains("Xmla") || providerName.Contains("Adomd")))
        {
            for (int i = 0; i < 5; i++)
            {
                button.Items.RemoveAt(i);
            }
        }
    }
}

How to reproduce: check the attached project and select an item from the drop-down list

The new API would allow some of the default functions to be removed and custom aggregate functions to be added. At the moment the dialog can be modified like this:

Public Class MyAggregateOptionsDialog
    Inherits AggregateOptionsDialog

    Private availableAggregateFunctions As IList(Of AggregateFunction) = New List(Of AggregateFunction)() From {
        AggregateFunctions.Sum,
        AggregateFunctions.Count,
        AggregateFunctions.Average,
        AggregateFunctions.Max,
        AggregateFunctions.Min,
        AggregateFunctions.Product,
        AggregateFunctions.StdDev,
        AggregateFunctions.StdDevP,
        AggregateFunctions.Var,
        AggregateFunctions.VarP,
        New SqrtSumAggregateFunction()
    }

    Public Overrides Sub LoadSettings(aggregateDescription As PropertyAggregateDescriptionBase)
        MyBase.LoadSettings(aggregateDescription)

        Dim listAggregateFunctions = DirectCast(Me.GetType().BaseType.GetField("listAggregateFunctions", BindingFlags.NonPublic Or BindingFlags.Instance).GetValue(Me), RadListControl)
        listAggregateFunctions.DataSource = availableAggregateFunctions
    End Sub
End Class

To reproduce:
Try setting the value in the CellForamting event. 

Workaround:
class MySpreadExportRenderer : SpreadExportRenderer
{
    public override void SetCellSelectionValue(DataType dataType, object value)
    {
        base.SetCellSelectionValue(dataType, value);
        if (dataType == DataType.Number)
        {
            CellRange range = ((CellSelection)this.GetCellSelection()).CellRanges.ElementAtOrDefault(0);
            double d;
            if (double.TryParse(Convert.ToString(value), out d))
            {
                var cell = ((Worksheet)this.GetWorksheet()).Cells[range.FromIndex.RowIndex, range.FromIndex.ColumnIndex];
                cell.SetFormat(new CellValueFormat("#,##0.00"));
                cell.SetValue(d);
            }
        }
    }
}