Tom is demoted from his position as Consigliere. So the questions I have are:

(i) How did Tom know Barzini was going to make another attempt at Michael?

(ii) Why isn't Tom at the baptism?

(iii) What reason did Tom have to be going to the "meeting" in Brooklyn?

(iv) Is Tom unhappy at them having to kill Tessio?

(v) Is Michael "throwing a bone" to Tom by allowing him to witness the interrogation and killing of Carlo because he knows Tom was close to Sonny.

It just seems that Tom was portrayed as not being completely out by the end of GFI with no clear explanation of what transpired between Vito/Michael talking to him and the funeral.

To be honest, I don't have access to the book right now nor can I remember if it sheds any light.

It sheds a little. The meeting directly after Vito's funeral includes, "...Tom Hagen forsaking his strictly legal role to rally around in this crisis...", then he stays on after everyone else has been dismissed and he and Mike assess the situation. From that point on, he seems to be functioning as consigliere again.