1 - What is the basic method of maintaining anonymity?
Public keys are not linked to an actual identity, no certificate in use. This maintains some anonymity.
2 - What additional method does Satoshi suggest?
Satoshi suggests using a new key pair for each transaction as an additional firewall.
3 - What weakness does this additional method have?
When multi-input transactions are in use, as is the case for exchanges, which holds a collection of input transactions. This links the input transaction to one entity, the exchange.