If I have a jailbroken iPad and upgrade the OS to the newest version, It won't be jailbroken anymore form what I understand. So what happens to the jailbroken apps? Do they remain on the iPad in a state where they won't work? If I jailbrake the new OS, will they then start working or will I have to download everything onto the iPad again?

I would rather not lose everything. Is there a way to backup a jailbroken iPad so that you can restore it like iTunes does?