- How can I do so that the author's full name, and not just the icon with the photo and initials, appears visible explicitly  (not only by mouse) near to each note ?  Just as it appears in the History section or at the top of the note in the Activity stream box  ?

This is not possible.
We used this design to leave the most room possible for the notes.

- Could I make the Notes section appears immediately by default, therefore instead of the Description section, in the Area section, preferably only for the Action element  (if not, it does not matter, for all elements with Notes section) ?  Even by my direct intervention on some code file (what ?) or directly on the database.  I seem to have read somewhere on the forum that this could only be done via Screen Customization Plugin: do this plugin offer a selection  option for default first section in detail area ?

You could possibly move the Notes section first in the description of fields.
Note that this cannot be done through Screen Customization plugin, as this tool cannot move sections "Notes, "Attachments" and "Links".
Also note that moving (changing code) this section first may have unexpected side effets (possibly that's why the plugin cannot move them)

- I saw that possible states for the microactivities within a Todo list are only 3: "In progress", "Done" and "Closed". How could I add another state, eg. ToDo or Paused (states that are all possible with different workflows in the status under Treatment area of all elements)  ?

This is not planned.
IKt would require some coding

- I don't have Mobile plugin, yet,  but on demo.projeqtor.org/mobile it seems to me that  author of the note is completely missing: only the written text and that's it !!!   Also I don't know if is possible "displaying notes in discussion mode". These would be essential also on the Mobile version, as well as  to enhance all the features relating to communication between users.

We could add the author of note on mobile. It would be an improvement.
For the discussion mode, mobile devices have small width that is not fitted to multiple indentations of discussion mode.
We tried it, it was awfull, soi removed it.

- It is right that Mobile version is limited. Also you are to the first version and the features are numerous, but do you plan to add the Detail / ToDolist section soon, in addition to the Notes and Attachments of elements ?

It's not planned yet, but it could be an improvment.

Could you kindly tell me what are exactly the parts of code, file or files, I could eventually try to intervene to move Note section (of only Action element, preferably, or all elements) to the beginning ?
I am confident in the important addition of the known Note's author name, in an upcoming Mobile version and also addind of Detail/ToDolist section

Thanks you very much
Luigi Milite

It must be changed in model/ActionMain.php, or better in model/custom/Action.php to use the plugin inheritance capacity.

Hello,
thanks again for replies. Staying on this topic and messaging subject,  could I also ask you why author of message does not appear in the  Messages section  on Dashboard ?  It is true that this type of messages are generally sent by one system administrator, but INFO messages  could be sent to all department’s employees  from one of the many manager  of  company. Sometimes even from one employee to another one, similar to email.
Possibly, could I add a new field: “sender” or "issuer" of message, to the message list on Messages page, through Screen Customization plugin or otherwise ?     Now is only  possible visualize User = "destination" field of the message, not "sender" user !
 

Hello,
thanks again for replies. Staying on this topic and messaging subject,  could I also ask you why author of message does not appear in the  Messages section  on Dashboard ?  It is true that this type of messages are generally sent by one system administrator, but INFO messages  could be sent to all department’s employees  from one of the many manager  of  company. Sometimes even from one employee to another one, similar to email.
Possibly, could I add a new field: “sender” or "issuer" of message, to the message list on Messages page, through Screen Customization plugin or otherwise ?     Now is only  possible visualize User = "destination" field of the message, not "sender" user !

As you correctly mention, these are technical messages dedicated to global communication, not some chat system.
Unfortunately, you cannot custom these messages with the plugin.

I am a little sorry, obviously I say this as very interested in all aspects of communication (but I think we are many), still considering Projeqtor messaging system quite valid despite being a PM tool. It would take very little, that is just communication sender's author name, better if the date and time of sending too, to make the messaging on the Messages box, almost a rudimentary mail or communication system not correlated to specific activities or other project elements (outside the activity stream) . . .

It would take very little

Possibly, all is question of priorities 

a rudimentary mail or communication system not correlated to specific activities or other project elements (outside the activity stream)

This would not be so little, as visibility of notes is defined through visibility of item.
So changing this design would lead to complex security / access changes.