When you create a new table, and you insert it with some rows, but you get these error. It’s mean that your new table can’t be write. Otherwise, your other old tables is fine, writable.
Instead of change your mysql folder permisson, you might to:
Change your new table Storage Engine. You can do it on Operation menu on your phpmyadmin or other mysql visual administrator. Compare it with your old tables Storage Engine.
In my case, my new tables Storage Engine is default set to MRG_MYISAM. My old tables is InnoDB. So I change my new table Storage Engine to InnoDB, then it works, writable.