_ A moderator can see if a user have decline or accept the demand of an other user to be in contact with him ? The button Is for connection request
I want to be informed (the moderator), by notification (email) or in a dashboard, when a user have accept or decline a connection request of an other user.

Only way to do that is using CB Auto Actions to send an email to moderators when a connection request is made, accepted, or rejected. There are no notifications to moderators for other users connection requests built into the connections functionality.

_ Is it possible to limit theses "relations directes" to one by user ?

Only allow a users to be connected to 1 user at a time? There's no functionality for that, but you can probably force it using CB Auto Actions by interrupting the connection request accept if they already have a connection.