Anonymity

It's hard to imagine the Internet getting segmented airtight.  It would have to be a country deliberately and totally cutting itself off from the rest of the world.

Any node with access to both sides would automatically flow the block chain over, such as someone getting around the blockade with a dial-up modem or sat-phone.  It would only take one node to do it.  Anyone who wants to keep doing business would be motivated.

If the network is segmented and then recombines, any transactions in the shorter fork that were not also in the longer fork are released into the transaction pool again and are eligible to get into future blocks.  Their number of confirmations would start over.

If anyone took advantage of the segmentation to double-spend, such that there are different spends of the same money on each side, then the double-spends in the shorter fork lose out and go to 0/unconfirmed and stay that way.

It wouldn't be easy to take advantage of the segmentation to double-spend.  If it's impossible to communicate from one side to the other, how are you going to put a spend on each side?  If there is a way, then probably someone else is also using it to flow the block chain over.

You would usually know whether you're in the smaller segment.  For example, if your country cuts itself off from the rest of the world, the rest of the world is the larger segment.  If you're in the smaller segment, you should assume nothing is confirmed.