Hi,
The error "Unknown column 'hikam_vendor.accepted_cities' in 'where clause'" indicates that something is trying to use a column "accepted_cities" in the table hikamarket_vendor. However, there is no such column in HikaMarket and no MySQL query in either HikaShop or HikaMarket on that column since it doesn't exist by default.
So I'm thinking that you're using the plugin vendor location filter from HikaMarket and that you configured it to use a custom vendor field that you didn't recreate or that was deleted for some reason.
The check database button won't help in that case. You need to fix the configuration of that plugin.
Regarding the error with the check database, that's because you have several "helpful" votes coming from the same IP address for the same vote (which was a bug from an old version) but it's not possible anymore.
And when HikaShop tries to add a rule to the table to be up to date, it fails because of the doublons.
It's not a problem. You can just ignore it. If you really want to fix it, you would have to delete the doublons in the hikashop_vote_user table via your phpmyadmin.