our separate extension Content Statistics can record this data.

Great...

What does the Backend component for complete activity log reports do? Shows statistics graphically?

Will the Content Statistics Professional allow me, from the backend, to download a file that may be later imported, for example, in Excel?

Hi Mario,

the backend component shows, line per line ("action per action") the activity recorded ("user X played song Y on date and time Z")

the non-extended version does NOT have this backend interface, which is the one that includes the CSV download file (that you can import into Excel)
for this, you need the EXTENDED version.

here the table to compare packages: http://www.joomlathat.com/content-statistics/different-packages

Ok, got the module from you.

I am running Joomla 3

The are two modules, one without _admin at the end and another with _admin at the end.

Should I install just one of them or both?

the _admin is for the admin interface, you can install or not, depending on if you need it.
most important is to install the plugins and the component. please be sure to read the installation instructions.