How to create a tick list which one role can alter for 'lesser' roles to see?
From the interface that you have outlined, I could see that the 'Flag' module might be really nice for the administrator and user to interact with this kind of list.  In a list of nodes, flags would allow in place editing, changing the status, without going into each individual node.

You could configure the names of flags, status, and transition.  It would also be possible to assign permissions as to who has permission to change flags between states, and to allow users to change some of the flags themselves.

http://drupal.org/project/flag

To restrict what is seen by the users in the lists, perhaps you could build two similar views blocks: one showing all of the nodes (for administrator), and the other filtered only to show those with flag set to 'show' (for normal users).  

The options in each view can be configured to selectively shown each block only to the appropriate role, and then both blocks could be embedded at the appropriate place.

Please note, that is not really enforcing permission to view the hidden nodes, and that a user could find them if they really try hard. It's just being selective about what is shown in the lists.

I was not able to quickly spot an existing module in drupal.org which would set node access by flag status.  You may have some luck with some further searching.  

However  you can use 'Rules' to take actions on flag changes.  I think you might be able to pull something together by setting up a series of rules which then assign individual node permissions using 'content access' or another node access module of your choice when the show/hide flag changes state.

Otherwise you could use node_api and write your module to enforce your particular access rules  based on flag status.