Sub AddSect()
'add a new section at end of document
Dim char As Range
'set char to the last character in the document
Set char = ActiveDocument.Range.Characters.Last
'With sections collection object, use add method to add a section
ActiveDocument.Sections.Add Range:=char
End Sub

About your second question, what do you mean by "current page"?  My
understanding is that Word isn't really designed around pages.  As I
understand it, Word sees a document as a collection of sections, ranges,
paragraphs and characters.  If the "current page" is just the one where the
cursor is blinking, then why not just use the insert menu to insert a break
at the cursor?  If the current page is something else, I think you need to
define it in terms of a range or a section or something Word understands.