Return Anonymous Type from a Function

No you can't return an anonymous type from the method. For more info read this MSDN doc. Use class or struct instead of an anonymous type.

You should read blog post - Horrible grotty hack: returning an anonymous type instance

If you are using framework 4.0 then you can return List<dynamic> but be careful to access the properties of anonymous object.

private List<dynamic> GetRowGroups(string columnName)
{
var groupQuery = from table in _dataSetDataTable.AsEnumerable()
                             group table by new { column1 = table[columnName] }
                                 into groupedTable
                                 select new
                                 {
                                     groupName = groupedTable.Key.column1,
                                     rowSpan = groupedTable.Count()
                                 };
    return groupQuery.ToList<dynamic>();
}

No, you can't return an anonymous type directly, but you can return it using an impromptu interface. Something like this:

public interface IMyInterface
{
    string GroupName { get;  }
    int RowSpan { get; }
}

private IEnumerable<IMyInterface> GetRowGroups()
{
    var list =
        from item in table
        select new
        {
            GroupName = groupedTable.Key.column1,
            RowSpan = groupedTable.Count()
        }
        .ActLike<IMyInterface>();

    return list;
}

Just use and ArrayList

    public static ArrayList GetMembersItems(string ProjectGuid)
    {
        ArrayList items = new ArrayList(); 

              items.AddRange(yourVariable 
                        .Where(p => p.yourproperty == something)
                        .ToList());
            return items;
    }

Use object, not var. You'll have to use reflection to access the properties outside the scope of the anonymous type though.

i.e.

private object GetRowGroups(string columnName) 
...
var RowGroupList = new List<object>();
...

From C#7 you can return a list of tuples:

private IEnumerable<(string, string)> GetRowGroups(string columnName)
{
    return from table in _dataSetDataTable.AsEnumerable()
           group table by new { column1 = table[columnName] }
           into groupedTable
           select (groupedTable.Key.column1, groupedTable.Count());
}

You can even give the members of the tuple names:

private IEnumerable<(string groupName, string rowSpan)> GetRowGroups(string columnName)
{
    return from table in _dataSetDataTable.AsEnumerable()
           group table by new { column1 = table[columnName] }
           into groupedTable
           select (groupedTable.Key.column1, groupedTable.Count());
}

However you need System.ValueTuple from the Nuget Package Manager.

Anyway I suggest to give things a clear name that includes what their purpose is, in particular when this is part of a public API. Having said this you should consider to create a class that holds those properties and return a list of that type.