Rewriting the blockchain? The main bitcoin blockchain (the chain that miners choose to work on) is the chain with the most proof of work ("heaviest" chain). Currently, the cumulative proof of work on the bitcoin main blockchain is about 2^94 hashes. 

I have a few questions here:

(1) How is the cumulative proof of work on a bitcoin chain calculated? Are they calculated by checking the timestamps (and thus the difficulty)? 

(2) Let's say an adversary has an alien supercomputer he stole from Area 51. He uses this alien supercomputer to rewrite the entire bitcoin blockchain from the genesis block - by mining a private chain that is heavier than the current chain. Does the current bitcoin network have any method of defending against this kind of attack? (I know that checkpoints can prevent such an attack, but checkpoints are no longer in the current bitcoin protocol, as far as I know)

(3) What would be the consequences of a bitcoin blockchain rewriting attack? An instant crash in bitcoin price? Would bitcoin be essentially dead forever, or does the bitcoin network have a way to recover and go on?
There's no need to consider the timestamps in order to know the difficulty. The difficulty is stored in the blocks.
This is a bit speculative but in the past such threats have been discussed, more along the lines of the hash function being hacked, and I think in such cases there will be a large consensus to hard fork. If the hypothetical threat you're describing is basically an adversary with infinite free power then most like PoW would have to be abandoned. Let's worry about that we get there. ;)