Is it possible for learners and teachers to receive a notification by email when someone post a comment or question on the forum ?
How to ease the discussions between learners ? How to easily animate the learning community (chat, FAQ, best practices discussion). Is there a functionnality for social learning or and existing API or plugin ?
yes of course, you just need to enable the appropriate event (under Administration > settings > event manager) to make those notifications be sent.
Concerning social learning functions, Forma Lms has a forum, a chat, a Wiki function and a (albeit quite primitive) "projects" function. There is also a "repository" that you can use to have users upload their homework, for example.
natively it's not possible to add new items in the header area. What you easily do is to create "external pages" under Administration>contents>web pages. If you create a web page there you can insert whatever you want, including a link.
It will be displayed under the footer of the LMS.