I'm having the exact same problem. Everything is not showing up where it should be but is in 'monitoring'. So, in summary;
Having dropped my tables and started with a backup that I know was working, if I do not enter the Home Category manually, I get a PHP error thrown letting me know that there is a problem.
Categories input manually or by import shows as successful but the categories do not show up anywhere in the back office other than Catalog:Monitoring. My understanding is that they should show up when I am in the back office Catalog:Categories.
When I "View My Shop", the results are even more puzzling. One of the categories, which is available in the 'root' dropdown menu, does not show up at all on the horizontal menu bar.
No categories are showing up, at all, in the footer area.
I've attached some files that will perhaps give you perspective and help in finding a quick resolve of this issue.