Thank you.
That means that the database structure could be updated properly last time you updated HikaShop.
You need to go in the database administration tool provided by your hosting company ( it's likely to be PHPMyAdmin ) and run the query :
ALTER TABLE `jos_hikashop_product` ADD `product_last_seen_date` INT UNSIGNED DEFAULT 0
That will solve the query error on the front end.
For the characteristics issue, could you make sure that you don't have any variant in the "manage variants" area of your product, then, delete the two characteristics, save your product, and add them again ? Then, the system should automatically recreate the variants properly.