If this is already happening how does it handle long delays i.e. one month.
The same way that it handles short delays.
What happens to bitcoins created and spent in this case? Obviously the transactions are voided, but the economic activity has already taken place and the money would have been distributed through the network as wages, purchases or gifts.
If coins are created during the split, and the split lasts longer than 100 blocks, then those coins and all the transactions that depended upon them in the minority chain simply cease to exist after the merger. There is no other way to do it, unfortunately. If the minority blocks were permited to exist, block splits would become a profit vector in their own right, breaking the 21 million coin limit with ease.
Seems that for areas of frequent connectivity dropouts it may be better to have their own currencies and block chains with an exchange rate.
If you have frequent connectivity dropouts, you probably shouldn't be trying to mine at all. But blockchain splits should never be an issue, as it's trivial for a watchdog process to detect a blockchain split, particularly when it's on the minority side of the break. As large as the Internet is, a near even network split, resulting in a near even block discovery rate on both sides of the divide, is astronomicly unlikely. If the rate of block discovery, from your perspectives, drops by more than half then users should be suspending the acceptance of new coins created since the division anyway.
Is there any documentation for how block chain management works
Have you read the white paper?