There is not going to be any aircraft up there in the declared TIBA airspace that has not submitted a flight plan so that is one way ATC at either end can look ahead and see what is out there for passing on traffic information purposes if required.
Nope, they can give you nothing more than an appreciation of what is already on their screens. This is particularly dangerous near the FIR boundary, between BN and ML centres, as the information displayed on the other side of the boundary is at best inaccurate; at worse non existent.
Getting a Snapshot from Melbourne Sectors or SY TCU about what's over the OCN is totally a no no, and as an ATC I can state we have not had any training in what is or isn't appropriate to say. I wouldn't be giving you any advice about what's over the water, cause I don't know, and probably anything I did say could give you a false sense of security.
As for offsets etc; everything is fine until the conflict is also offsetting the same altitude difference or the other side of track; and then it offsets only solve opposite traffic really. With crossing tracks offsets count for zip.