I've no access to other accounts but other accounts can access mine!

Normally, no one should be able to access another's account information, via the GUI (graphical user interface); although, there are ways via the Unix command line interface for admin users/super users to do that. Need more details. Are your partner's and son's accounts admin user accounts? What are the ownership and permission settings on all three accounts? Open /Users, select one, and CMD+I to determine.

Finally, click on the Desktop, Finder->Help->MacHelp->Index and search for accounts to see the details.

There's a disconnect here. Each account should be owned by user, not you (BT). Non-admin accounts shouldn't show Admin as group, but the lad's account shows you as owner and group as Admin. Additionally, Others should be read only on all accounts. What you can do, as admin, is delete the screwed up accounts, saving the data, recreate the accounts as desired, log into them, mount the appropritate saved data disk in /Users/Deleted Users/, and copy the stuff back.

Somehow, the permissions settings on your home folder's subfolders got hosed. This can happen if you delete them and then manually recreate them.

You can fix it by logging in to your user account, opening Terminal, and entering this:

chmod go-rwx ~/Documents ~/Movies ~/Library ~/Pictures ~/Desktop

Other users should now be locked out of all of those.

Sounds like the permissions have been changed - for example, access allowed for the admin or an old user's group. Normally, a user (even an administrator) does not have access to another user's files. You don't go into another account to get files, that is what the Shared and Public folders and drop boxes are for:

The /Users/Shared folder is used to share files between all users (it has read/write access by others), and a user's Public folder is for (read only) files that the user wants to share with others. The drop box in a user's Public folder is to pass files to that particular user.

Check the permissions of various user folders - normally they are:
The /Users folder is owned by the system, with read/write access for the admin group and read only for others.
A user's home folder has read/write permissions for the owner, and read only for their group and others (read only is to allow access to their Public and Sites folder).
The Public and Sites folder in a user's home folder has read/write permissions for the owner, and read only for their group and others.
All other folders in a user's home folder have read/write permissions for the owner, and no access for group or others. Note that if folders or files are added to the root level of a user's home folder, the permissions should be changed to no access by group or others, otherwise they can be read by others (folders inherit the same permissions of the user's home folder).