My question is how the number of RAM modules affects the performance on a computer. For example, if all other things are equal, will a computer with two 256 MB modules perform better or worse than a computer with a single 512 MB module? I am assuming, of course, that all of the modules have the same CAS latency and other characteristics. I know that it is much faster two have data distributed across two hard drives, because the computer can perform I/O operations on each hard drive independently, but I'm not sure if this is possible to do with memory.

I believe only if the motherboard supports dual channel, which many do, not sure how much of a benefit it gives, but I hear its worth it. You get twice the twice the bandwidth to throw things back and fourth like you said with the hdds, have to make sure the mobo supports it, and usually has to be put in the right slots (like slot 1 and 3 or whatever the manual says) as well as the same size and even helps to be the same brand and batch I hear as well. But if its not a dual channel mobo, don't think it will matter, but not 100% sure.

hard to tell, but my answer would be "whatever it does, it is probably not something you can notice". RAM latency are in miliseconds, so even if you win/loose some it doesnt matter much, if you want to improve performance, you better take a look to your hard drives

In theory, I suppose you could argue that 2 RAM create some "parallelism" mean that you computer could read and write to RAM at the same time (if your board support dual channel ram access), however I have no clue if this is better on 2 ram or if it works as well on a single one.
But you could also argue that the second ram will be slightly farther than the first one from the CPU, mean the access time would be slightly worse, slowing down both RAM.

But again, all this are therories, in fact, it doesnt matter, RAM is never the bottleneck on your computer.