If the browse button is greyed out, that means there's no data in the table to be browsed
If you're not archiving any emails then that won't matter. But it begs the question of "how" did it disappear? If it's missing during a database-upgrade, you may run into errors that will cause upgrade challenges since it will have to abort mid-stream. Thus I suggest that you recreate it perhaps from a backup.
That's normal, and can be ignored.
"key 1" is probably the primary key on the table, which would be the banners_history_id field.
Since the "insert" statement doesn't mention that field (and this is normal and desired), it is expecting the auto-increment attribute of that field to automatically select the correct next number. So, if you're getting that error on that table, it means the banners_history_id is not set to autoincrement.
Same issue as mentioned above for banners_history table.
If it was working flawlessly until a certain date, then unless it's something you or your staff have done to the site, your first line of support for these odd database issues should be your hosting company -- so they can investigate what may be wrong on the server to break the autoincrement funcitonality.
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