So assuming that's all accurate, if I set it on solo and start working on a block and stop working on it before it's solved, that doesn't benefit the system in any way, right?
It turns out not to have benefited, but you didn't know that before you tried. It's like asking if buying fire insurance is no benefit if you don't have a fire.
In fact, that really brings up tons more questions about soloing. How could that possibly work? I take it I'm not just grabbing a fresh block and saying "I'll handle this one" and then taking like months to finish it and whatever poor guy had his transaction included in that block isn't gonna have it go through until it's done. That wouldn't work real well.
No, everyone tries to generate the next block. If you do it first, you win. (Oversimplifying a bit.)
And why don't transactions take 10 minutes to complete? I heard they're close to instant. But if your transaction has to be put in a block, completed, and have that block added to the chain before the transaction is official, wouldn't that take 10 or less minutes randomly?
It depends on your definition of 'complete'. You might consider the transaction complete as soon as it has been accepted by the network even if it hasn't gotten into a block yet on the reasonable belief that it will get into a block shortly. Strictly speaking, certainty is never possible, but then the Earth could get blown up in five minutes.
And if there's only ever one block being processed at a time every 10 minutes and completion results in no more than 50 coins, everyone is working on the same block, right? Cuz I thought pools and soloers get their own block. If the resulting payout is in fact 50/block, do pools and soloers just take turns or what? Or the first pool to solve it gets 50 and nuts to the other who were working on it?
Everyone tries to generate the next block. Each miner has their own 'skeleton' that they're trying to turn into the next block to avoid wasted effort. Whoever does so first (again, oversimplifying a bit) wins, their block becomes part of the public hash chain, and they get 50 bitcoins.
Really no effort is wasted. Even if you fail to find a block, the statistical difficulty you added to the public hash chain makes it that much more difficult for anyone else to launch a double-spending attack. To make such an attack work, the attacker must generate blocks faster than the rest of the world combined. Every additional miner makes the attack that much harder.