As I thought, that’s probably where your incorrect timestamp handling is coming from.
I don’t know. This is something which should be handled by Zammad, with database changes/migrations during installs/upgrades. It might be solved automatically when performing the upgrade path to 6.3. I don’t know the history of the datatypes of these columns and if/when/why they were changed at some point.
No, you shouldn’t need to touch your database version in order to be able to fix this.
Also, you probably shouldn’t touch the column by yourself, as this might lead to even more unexpected behaviour in Zammad. I would suggest what MrGeneration already said: to upgrade to 6.3 and see if the issue is still present. If it is, you might need to manually perform a data migration and DDL change.