Is it possible to set permissions for list items based on one people picker field item (Created by/ Admin column/ Viewer column)? It is possible to make a list only allow users to do some the items they have created.
Not possible. You need to break permission inheritance and assign unique permission to make it work.
You can workaround this by creating views. The view should display only items created by current user. Thus you can restrict user to edit only items created by him/her.
The drawback is the user will not see other items created by other users.
Setting permission is OOTB not possible. But you can restrict the user to only work on their items. Goto List Settings -> Advanced Settings -> Item-level permission!