They don't seem to be similar in time-to-solve, number of transactions, total BTC sent, or block size. Is there any standard way in which blocks are defined while they are being solved
https://en.bitcoin.it/wiki/Blockshttp://james.lab6.com/2012/01/12/bitcoin-285-bytes-that-changed-the-world/is anyone free to group the most recent transactions (coming after the last solved block) into a block and try to create the special zero-prefix SHA256 hash? So that I might be trying to solve a block with 137 transactions, but someone else is trying to solve a block with just the first 56 of those 137, leaving the remainder to be solved as part of another block?
Yep. As a matter of fact, you can even work on a block that has only 1 transaction (the coinbase transaction that pays you the block reward when you solve the block), and no others. Here's an example:
http://blockchain.info/block-index/381211/00000000000000fded04b4c7e2c9936310f5642e2dd9a834187a8afa4eba14ec