Excel VBA Event Handlers

I always recommend this when using Worksheet_Change

1. You do not need the sheet name. It is understood that the code is to be run on current sheet unless you are trying to use another sheet row as a reference as correctly mentioned by brettdj in the comments below.

2. Whenever you are working with Worksheet_Change event. Always switch Off events if you are writing data to the cell. This is required so that the code doesn't go into a possible endless loop

3. Whenever you are switching off events, use error handling else if you get an error, the code will not run the next time.

Here is an example

Option Explicit

Private Sub Worksheet_Change(ByVal Target As Range)
    On Error GoTo Whoa

    Application.EnableEvents = False

    '
    '~~> Rest of the code
    '

LetsContinue:
    Application.EnableEvents = True
    Exit Sub
Whoa:
    MsgBox Err.Description
    Resume LetsContinue
End Sub

So using the above, your code becomes (UNTESTED)

Private Sub Worksheet_Change(ByVal Target As Range)
    Dim rowCount As Long

    On Error GoTo Whoa

    Application.EnableEvents = False

    With ActiveSheet
        rowCount = .Cells(.Rows.Count, "A").End(xlUp).Row
    End With


    If Not Intersect(Target, Range("M3:M" & rowCount)) Is Nothing Then
       MsgBox ("Hi")
    ElseIf Not Intersect(Target, Range("T3:T" & rowCount)) Is Nothing Then
       MsgBox ("Hi")
    ElseIf Not Intersect(Target, Range("X3:X" & rowCount)) Is Nothing Then
       MsgBox ("Hi")
    ElseIf Not Intersect(Target, Range("AB3:AB" & rowCount)) Is Nothing Then
       MsgBox ("Hi")
    ElseIf Not Intersect(Target, Range("AI3:AI" & rowCount)) Is Nothing Then
       MsgBox ("Hi")
    End If

LetsContinue:
    Application.EnableEvents = True
    Exit Sub
Whoa:
    MsgBox Err.Description
    Resume LetsContinue
End Sub

EDIT:

Regarding your 2nd question. As I mentioned in the comment above, you can use a Public variable to check if the worksheet change event is being caused by the workbook open.

Place this code in a module.

Public WasWbOpened As Boolean

Place this code in the workbook code area

Option Explicit

Private Sub Workbook_Open()
    WasWbOpened = True
    '
    '~~> Rest of the code
    '
    WasWbOpened = False
End Sub

And change your worksheet change event to

Private Sub Worksheet_Change(ByVal Target As Range)
    If WasWbOpened = True Then Exit Sub

    Dim rowCount As Long

    On Error GoTo Whoa

    Application.EnableEvents = False

    With ActiveSheet
        rowCount = .Cells(.Rows.Count, "A").End(xlUp).Row
    End With


    If Not Intersect(Target, Range("M3:M" & rowCount)) Is Nothing Then
       MsgBox ("Hi")
    ElseIf Not Intersect(Target, Range("T3:T" & rowCount)) Is Nothing Then
       MsgBox ("Hi")
    ElseIf Not Intersect(Target, Range("X3:X" & rowCount)) Is Nothing Then
       MsgBox ("Hi")
    ElseIf Not Intersect(Target, Range("AB3:AB" & rowCount)) Is Nothing Then
       MsgBox ("Hi")
    ElseIf Not Intersect(Target, Range("AI3:AI" & rowCount)) Is Nothing Then
       MsgBox ("Hi")
    End If

LetsContinue:
    Application.EnableEvents = True
    Exit Sub
Whoa:
    MsgBox Err.Description
    Resume LetsContinue
End Sub

You have several issues

1. As per Sid's comment you should use rowCount = ws.Cells(ws.Rows.Count, "A").End(xlUp).Row
2. You should be using Set ws = Sheets("datasheet") not Set Worksheet = "datasheet"
3. Your Else statements are causing errors as they are orphaned. If you want to exit on the first "Hi" rather than continuing to test you should try something like this

Sid has covered your other point. You can use a Boolean variable for this

updated code

this tests the intersect on columns M, T, X, AB and AI from row 3 to row rowCount in a single line

Private Sub Worksheet_Change(ByVal Target As Range)

Dim ws As Worksheet
Dim rowCount As Long

Set ws = Sheets("datasheet")
rowCount = ws.Cells(Rows.Count, "A").End(xlUp).Row

If Not Intersect(Target, Range("M3:M" & CStr(rowCount) & ",T3:T" & CStr(rowCount) & ",X3:X" & CStr(rowCount) & ",AB3:AB" & CStr(rowCount) & ",AI3:AI" & CStr(rowCount))) Is Nothing Then MsgBox ("Hi")

End Sub