You only need to keep the latest version of the patches in the Scan folder unless your company requires the older version. Under the Scan folder is a Replaced folder. This folder contains all of the patches that have been replaced by a newer version so you can move them to the Do Not Scan folder.
Patch Manager will not install Adobe Reader if an older version is not currently installed because this is Patch Manager. Patch Manager has to detect the patch is needed on the client or it will not install it. To install applications on computers, you need to create a Distribution Package to push it to the clients.
The patches that have _Upgrade in the ID will upgrade older version to the version in the patch. The patch that does not have _Upgrade in the name, will only update the sameversion to the current patch level.