Is the current number of confirmations visible somewhere in the raw block? Is the current number of confirmations visible somewhere in the raw block output created by blockexplorer or blockhain.info? 

Is this information available in the raw stream or is the number of confirmations always "live" calculated by counting the confirmations and not "saved" in the raw stream?
The number of confirmations is (height of most recent block - height of the block containing the transaction + 1). The contents of the specific block containing the transaction are fixed, while the number of confirmations keeps increasing, so the number of confirmations cannot be in the raw block data.