I just found a possible work-around for the original question. It isn't elegant, but it may work.
In each of your section headings (ie, in the text, which are then used to generate the TOC automatically), add a tab and the page number. You have to type in the page number manually, and I'm pretty sure it doesn't pay to get too fancy with placement, adjusting tab stops, etc.
Now, if you refresh the TOC, you get the page number separated from the heading by a tab. (When I tried to adjust the tab stops in the TOC, I got various errors.)
If you don't want the page numbers to appear next to the headings in the body of the document, highlight them there and change the text color to the background color of the document (usually white). The numbers are still there, and will still show up in the TOC, but you can't see them elsewhere.
Unfortunately, the page numbers won't flow as you edit the document, so do this just before final publication.
Again, not elegant -- not in appearance or in process -- but if you must have physical page numbers in a printed document, it should do the trick.
Best Answer
To split a table in Google Docs:
Select the bottom part of the table - everything below the point where you want the split.
Drag it below the table
Delete the empty rows that are left behind