1 - This is not attributable to the macro, and is probably the result of formatting variations in the question documents. I have introduced some formatting using styles from the normal template and replaced any instances of double paragraph breaks in the inserted documents with one break. That's as good as it gets without knowing the exact nature of the problem.
2 - That is much easier said than done, as the length of the questions is unknown. The modified version keeps the question heading with the first paragraph of the question.
3 - My fault - a misreading of the requirement. Fixed below.

Sub CreateTest()
Dim wdApp As Object
Dim wdDoc As Object
Dim oRng As Object
Dim LastCol As Long, LastRow As Long
Dim i As Long, j As Long, k As Long
Dim iQuestion As Long
Dim xlSheet As Worksheet
Const strDocsPath As String = "C:\Path\Docs\"
Const strPath As String = "C:\Path\"
    On Error Resume Next
    Set wdApp = GetObject(, "Word.Application")
    If Err Then
        Set wdApp = CreateObject("Word.Application")
        Err.Clear
    End If
    wdApp.ScreenUpdating = False
    Set xlSheet = ActiveSheet
    With xlSheet
        LastRow = .Cells(.Rows.Count, "A").End(xlUp).Row
        LastCol = .Cells(1, .Columns.Count).End(xlToLeft).Column
    End With
    For i = 2 To LastCol
        iQuestion = 0
        Set wdDoc = wdApp.Documents.Add
        For j = 2 To LastRow
            If xlSheet.Cells(j, i) > 0 Then
                iQuestion = iQuestion + 1
                Set oRng = wdDoc.Range
                oRng.collapse 0
                oRng.Text = "Question " & iQuestion & vbCr
                oRng.Style = "Heading 2"
                oRng.ParagraphFormat.keepwithnext = True
                oRng.collapse 0
                oRng.InsertFile Filename:=strDocsPath & xlSheet.Cells(j, 1) & ".docx"
                oRng.End = wdDoc.Range.End
                oRng.Style = "Normal"
                oRng.Text = Replace(oRng.Text, vbCr & vbCr, vbCr)
                wdDoc.Fields.Unlink
                Set oRng = wdDoc.Range
                'oRng.collapse 1
            End If
        Next j
        wdDoc.Range.Font.Reset
        wdDoc.Range.Style.Reset

        wdDoc.SaveAs2 Filename:=strPath & xlSheet.Cells(1, i) & ".docx"
        wdDoc.Close        'Optional
        DoEvents
    Next i
    MsgBox "Documents created at " & strPath
    wdApp.ScreenUpdating = True
lbl_Exit:
    Set xlSheet = Nothing
    Set wdApp = Nothing
    Set wdDoc = Nothing
    Set oRng = Nothing
    Exit Sub
End Sub