iOS update to 5.1 now all purchased apps are missing iPhone 3G

As long as the apps are still available in the store, and you use the same iTunes account as you originally used to buy them, then you should be able to re-download them for free : http://support.apple.com/kb/HT2519 . If you download them to your computer's iTunes you could then try restoring to your backup and see if that restores them and their settings/content - a backup doesn't contain the actual apps, just their content/settings, so for the restore to work fully iTunes needs access to the apps so that it can restore them.

As long as the apps are still available in the store, and you use the same iTunes account as you originally used to buy them, then you should be able to re-download them for free : http://support.apple.com/kb/HT2519 . If you download them to your computer's iTunes you could then try restoring to your backup and see if that restores them and their settings/content - a backup doesn't contain the actual apps, just their content/settings, so for the restore to work fully iTunes needs access to the apps so that it can restore them.