How does the Bitcoin payment forwarding at Blockchain.info work?
The fee for each transaction can be calculated using estimatefee API call. And yes, blockchain.info have to incorporate fee in every transaction, 0.0001 BTC being the minimum. One of the reasons attributed for the necessary fee deduction is the quick inclusion of the transaction in the next few blocks.
You can try creating a transaction with the outputs spending all of the inputs and not paying any tx fees. The client will throw an error stating insufficient priority.
Yes you can, but then are conditions apply. You can check out this link to clear things a bit more.