I'll try to answer some of your questions, but if what I say is a little too complicated, check out this website and watch the nice video. IMO it does a great job at simplifying BTC and mining:
http://www.bitcoinmining.com/1) Can you mine multiple currencies on 1 computer?
Yes, just not on the same GPU. I can mine BTC on one GPU, and LTC on a 2nd GPU, using two different instances of CGMiner.
2) What exactly does the hash rate mean? If blocks are being mined at 6 gh/s, do blocks get through twice as fast as they would if the hash rate was 3 gh/s?
You need to understand how BTC works. BTC mining is taking all the current transactions, adding a few pre-determined (and rapidly changeable) variables, and putting them thru a hashing algorithm (SHA-256). The speed number that people quote (150KH/s, 300MH/s, 2.5GH/s, or 100TH/s) is the number of times this process is repeated per second. My BFL Single is mining away 877MH/s, which means it's doing 877 million SHA-256 computations every second.
3) What is a 'mining pool' and how do you join one?
A pool is a way for miners to combine their efforts, and then split the rewards. Lets say you're a small time miner, who has a very small hashrate. You sign up for a pool (usually at their website), and use a miner software to point your GPUs or other hardware at their pool. If you have 1% of a pools hashrate, you get 1% of their BTC, regardless of whether you found the block or not. You get a small chunk of other people's blocks, but you agree to share your block with them if you find one.
4) Where do they block codes come from? I know transactions, but how does the pool get ahold of them?
When someone is mining, they are trying to find "shares". A share is a hash (that includes all the network transactions) that meets a pre-determined difficulty. For most pools, that difficulty=1. My BFL Single that I mentioned earlier mines at 877MH/s, and finds about 12 shares a minute.
A block is any share with a difficulty higher than the pre-determined network difficulty, which right now is 8.97million. Now these higher difficulty shares are very hard to find, and are quite rare, which is why people mine in pools.
The incentive for mining is that whoever does actually find a block (share with a high enough difficulty) gets granted BTC as a reward. These "newly minted" Bitcoins are not given from one place to another, but rather generated by the Bitcoin program. It's hard-coded that new Bitcoins can only be generated upon the discovery of a new block, and only to the person who found the block. This limits the supply of BTC, and offers incentive to mine.
5) Am I right about this?: Bitcoins are best and most popular to mine, but big pools means small payouts. Litecoins are mined fast, and are sold at a pretty good price. Devcoins are an easy coin to mine, and help to support the artistic and online development community. Feathercoins are easy to mine and may be worth something soon.
Bitcoins are by far the most popular crypto-currency out there. However, pool size does not limit your payouts. Larger pools will mean you get a smaller chunk of the block, but large pools find more blocks, so it evens out. Would you rather get $1 at the end of the day, or $0.10 10 times throughout the day?
Litecoin was designed to be "the silver to BTC's gold", and designed to run in parallel. Beyond those two, there are all sorts of alt-coins, not a lot of which are worth much.