Hi to myself,
I figured it out so I guess I'd post here some indication.
It is not possible to store or view data produced by a web application deployed locally using BPM free.
The way to do this is:
1) Develop process using BPM free
2) Open Web Community Platform
3) Create a new web project
4) Connect it to the cloud mysql database provided with Web Community Platform edition
5) --> synchronize the web project with the bpm project (https://www.webratio.com/learn/learningobject/how-to-quickly-synchronize-bpm-to-web-project-v-60?link=oln72ae.redirect&nav=14&cbck=wrReq0162)
It is not yet possible to see and browse business objects, but it is enough to add a new view, e.g.: a List which is associated to the bo of interest.