From first question:
Regarding an OSPF topology, when a link failed, some new LSA will be send, and flooded by all routers (or DR) in the area. What is the type of packet ? Link-state Update which contain these LSA ?
Link-state Update packet will be used. They are sent in two different ways:
- During adjacency db synch
- After adjacency is formed, if information about the link changes.
From second question:
Also, regarding the initialization phase of OSPF, the new adjacencies if performed with neighbors, so Database Description packets are transmit and then LS Request and then LS Update, do these LS Update packets are also flooded to all others routers in the area to announce the new link ?
Remember that all routers in the OSPF area need to have the same LSDB to ensure accurate routing knowledge. The update indeed has to spread.
RFC2328 states it as one hop at a time "A Link State Update packet may contain several distinct LSAs, and floods each LSA one hop further from its point of origination"