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Can a contract view the details of a transaction, given a transaction id?

More generally, what details of the blockchain is a given contract aware of?

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No, a contract only has access to the current state of the blockchain, and transactions are not part of state.

Specifically, these functions are available in Solidity for examining the current state:

block.coinbase (address): current block miner’s address

block.difficulty (uint): current block difficulty

block.gaslimit (uint): current block gaslimit

block.number (uint): current block number

block.blockhash (function(uint) returns (bytes32)): hash of the given

block - only works for 256 most recent blocks

block.timestamp (uint): current block timestamp

msg.data (bytes): complete calldata

msg.gas (uint): remaining gas

msg.sender (address): sender of the message (current call)

msg.value (uint): number of wei sent with the message

now (uint): current block timestamp (alias for block.timestamp)

tx.gasprice (uint): gas price of the transaction

tx.origin (address): sender of the transaction (full call chain)

<address>.balance: balance of the address in Wei

<address>.send(uint256) returns (bool): send given amount of Wei to address, returns false on failure.

Docs

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