What is the best way to backup all parameters in BackupExec before a fresh reinstallation on the same server ?

The problem you have is that when an in-place upgrade from one version of Backup Exec to another is performed, changes are made inside the
database which means you cannot just copy an 11D database into a 12.x server and expect everything to work.

There are three choices:
A) Copy the data and catalog folders to a safe location, then rebuild the server with 11D, copy the DB and catalog data back and then do an in-place upgrade to 12.x.
B) Upgrade the existing server to 12.x, then Copy the data and catalog folders to a safe location, then rebuild the server with 12.x, copy the DB and catalog data back.
C) Copy the data and catalog fodlers to a safe location, then rebuild the server with 12.x, copy the DB and catalog data back, but before you start all the Backup Exec services use BEMIG.EXE to upgrade the database (note you will need to start the SQL instance and a reg change is needed to use BEMIG) - suggest you do some reserach into using bemig.exe if you intend to use this method.

There are some impotant points that apply to all options
- if you are changing the installation paths as part of this work, then the Catalogs and Database location changes are not an issue, but the job logs for any old jobs will not be available in the GUI console, although will still be directly accessible from their folders in an informatted version.
- if the server name is being changed then an additional step to edit the server name reference inside the database will be required.