Untested code.  To modify the parents, use the Parent property.

Dim parent as TreeNode = node.Parent

Do While parent IsNot Nothing Then
 parent.Checked = False
 parent = parent.Parent
Loop

To go the other way, you need to recurse through all of the children:

CheckChildren(node)

Private Sub CheckChildren(node As TreeNode)
Dim child as TreeNode = node.FirstNode

Do While child IsNot Nothing Then
 child.Checked = True
 CheckChildren(child)
 child = child.NextNode
Loop

End Sub

While that does what you asked, I'm not sure it is what you really
want.  If you check a node, all of the children get set.  But if you
uncheck one of those children, only the child's parents, grandparents,
etc. will be unchecked, not the child's siblings.