The Availability settings tell the QVWS what client to use to open a document when clicked in the AP. Or whether a document can be downloaded as a QVW (not a good idea), printed, exported or used in a Collaboration Session.
At least one of the clients should be enabled. Do not use this to make a document disappear from your AP. There are better ways to do that (see above response)
If you have a Publisher, you won't need mount points. Define as many Source folders as you want, including those that contain non-publishable documents. When you defined reload tasks, omit a distribution for all documents that should stay away from the AccessPoint. They will be reloaded in the source folder, but won't move to the folder for published documents. Very simple.
In the root folder of the server on which the Access point is (QMC -> System -> Setup -> QlikView Servers -> Folders -> Root Folder). Check the NTFS permissions of every report you want to hide. If a user does not have at least NTFS read permissions on a file it will no visible in the Access Point.