email while creating a new group

Great ! I understand better the logic of substitution using variable thanks to the examples - Now i can customise the emails with substitutions

#1 Send an email to all registered users while creating a new group in a dedicated category
I wanted to add another condition to send email only if group is published (I suppose it is by using a [Custom Value ] EQUAL TO "YES" , I tried [Var1_Published], obviously not the good one....

#2  Send an email to all registered users while sending a message from the group

Yes I am aware of your recommendation to not use in a general case. In the case of our site, Group Owners are few dedicated users which should be responsible of what they send. The whole list of users are known subscribers of association. The use case is to send information to all about the group for everyone and not only those who joined the group. However I abandon the idea to trig an email to all based on group message because of #3. Maybe something to makes all users of the site to be automatically "joined user" (this is a specific need for 1 group category)  ?

#3 #3 Send an email to all joined participants while sending a message from the group
Yes OK, it is not CB AutoAction relevant
 

#1 Send an email to all registered users while creating a new group in a dedicated category
I wanted to add another condition to send email only if group is published (I suppose it is by using a [Custom Value ] EQUAL TO "YES" , I tried [Var1_Published], obviously not the good one....

That should just be the following.

Field: Custom > Value
Custom Value: [var1_published]
Operator: Equal To
Value: 1

Maybe something to makes all users of the site to be automatically "joined user" (this is a specific need for 1 group category) ?

You can force users into groups during registration with CB Auto Actions or you can use the Auto Join field that CB GroupJive provides in CB > Field Management to let them select a group to join during registration.