1) I might be wrong about this, because I haven't looked at the implementation too carefully, but in principle, I think forward and backward traversal of the chain should already be possible: as far as I'm aware, the unspent transaction output set needs to be rolled back if a recent part of the chain is replaced. If I'm not mistaken (and somebody please correct me if I am) the unspent outputs are only maintained for the "best block" and if this is replaced by an alternate chain, it isn't built from scratch.
class CBlockIndex has pointers pprev and pnext that point to the parent block and the child along the main chain. The main chain can be traversed forward and backward, but the entirety of the tree cannot. I see no reason why this can't be changed.
2) There is also a need to add hashes (or other identifiers) of newly discovered off-chain blocks into each block ("newly discovered" here means: not included inside any other previously reachable block). Nodes must then request such blocks if they do not already have them, and the propagation mechanisms / inv messages need to be adjusted accordingly.
Yes, this would also need to be done in order to implement your proof-of-work difficulty-adjustment algorithm, right? But it's not required for GHOST? I have not started looking into how to implement this. I am worried about the bloat that this would cause if the entire tree must be stored though. Have you looked into how your algorithm would fare if we ignored off-chain blocks for difficulty-adjustment?
3) I'm not sure what you mean by "the code to invalidate and discard blocks". Can you explain in more detail?
I was originally under the impression that the parts of the blocktree that are not on the main chain get deleted from memory, but now I see that what I was looking at was code to invalidate blocks if the header is not correct. I am not sure if the entire tree is kept in memory or if parts are eventually discarded.
By the way, I'm waiting to hear back from my friends before I email you back.