Is it possible to have many JIDs associated with one user. For example application installed on many devices which opened by the same user. When message is to be sent to the user all of the devices will receive it.
Yes, you can have many full JIDs associated with a single bare JID. So you have [email protected]/a [email protected]/b etc.
With Message Carbons (http://xmpp.org/extensions/xep-0280.html) your clients and server can negotiate the behaviour you describe.