CoreBOSBB

When I edit a task, and set a new follow up

system showed a pop up, correctly, but in the activities list system showed a date with zeros

See image  file in https://drive.google.com/open?id=1rhdWDQW8Vp4gVPaEluzB7V_7vsyTpMUL

I just tried this and it worked correctly on my install. Maybe you have a workflow that is losing the dates??

Also, review the "Create Calendar Follow Up" workflow which is the process in charge of creating the new record. Look at the online demo and make sure it is defined the same way.