1.how to find advertised routes to a particular neighbor
2.how to find received routes froma neighbour
3.how to find which neghbors are sending default routes - how the preferred one selected?
OSPF is link state:
each router in a OSPF area receives LSAs, OSPF data structures, as originated by the LSA owner inside OSPF packets
So reasoning in terms of routes and neighbors is not correct when we think of OSPF.
OSPF hasn't the split-horizon concept.
OSPF has a neighbor state machine: routing update in the form of LSAs are exchanged only with devices that have reached a certain level of neighboship.
The objective is that the database formed by the collection of all LSAs has to be complete and synchronized to allow to each router to execute the SPF algorithm using correct data.
So your neighbor will pass you all the routes in its DB.
So, the routes originated by your router include
the router lsa (one for Area)
other possible LSAs: network LSA if it is DR on a lan segment, LSA type 3 if it is an ABR and so on.
sh ip ospf database self-originated
if you want to know what IP subnets are originated by a router
sh ip ospf database adv-router OSPF-RID
you can find the ospf router id in the output of sh ip ospf on the neighboring router
sh ip ospf database external 0.0.0.0
this tells you what LSAs of type 5 for default net 0.0.0.0/0 are in the database
O E1 are preferred over O E2
so if an O E1 exists is preferred.
O E1 routes are compared based on the sum of the seed metric and the path cost to reach the ASBR (the default rotue injector)
O E2 are compared only on the basis of the seed metric
Hope to help