I'm going to take a shot at answering the questions about chromosomes, but I'm going to keep it simpler than most have. Keep in mind that there can be exceptions to anything, but by and large what I'm going to tell you will be true 99 and 44/100% of the time.
Each species has a fixed number of chromosomes that is the same for all individuals. The number of chromosomes can vary from 1 up to 132 (the highest figure I happened to find) and beyond, but probably very few species have over a hundred chromosomes. Since there are millions of species naturally many species will have the same number of chromosomes, but that's a matter of coincidence and is of no consequence. The number of chromosomes has little effect on what a species looks like.
If someone gave you two cells from two different species and you found that they had the same number of chromosomes, simply assuming they're the same species would be a big mistake.
Each chromosome is a long tightly wound tangle of DNA. Coded within the DNA are the genes. A specific gene always resides on the same chromosome, though it can move around somewhat on that chromosome during reproduction.
You are saying that all individuals of a species have the same number of chromosomes, but didn't someone here say that even within a species some individuals may have a different number?
Yes, someone did say this, and I have no idea why. While it is possible, it's potential for confusion makes it something that shouldn't be mentioned when merely introducing genetic concepts.
What on earth IS a chromosome anyway? It SEEMS like it's just arbitrary segments of DNA that COULD have been simply one long string instead. Is there any point to its being broken up into separate chromosomes?
I agree. I think you're asking a great question: what is the advantage of dividing a cell's DNA into separate pieces we call chromosomes. Presumably it came about because it provides some advantage (error reduction possibly?) Maybe someone out there knows the answer.
Do the different chromosomes have some identifiers that give them particular functions?
It is genes that code for the proteins that produce different functions. Each gene is comprised of a part of the length of the DNA strand that makes up a chromosome. Usually the coiled DNA strand that is a chromosome contains many genes.
it's very interesting that a particular gene is always located on a particular chromosome. Is this true across species in some overall general way, that genes for particular traits that are shared among different species show up on the same chromosome sort of more or less? Meaning for instance eye color which is always the one that comes to mind for some reason, is that gene or set of genes always located on a chromosome that is the same in all species where variations in eye color are a factor?
Checking with Wikipedia, there are many genes that play a role in determination of eye color. Choosing just one as an example, OCA2, for humans it always resides on chromosome 15, and almost always in the same place on chromosome 15. I wasn't able to find any information about where it is in other species.
This is the sort of frustrating information I've thought might be the case. So you are saying that genes on say Chromosome 12 can trade places with genes on Chromosome 8, I assume during meiosis -- I also assume it would be a comparable chunk size-wise? -- so that pretty much does in any idea that the chromosome can be definitively identified by its set of genes. Or is there nevertheless some rule to this sort of event, rather than the randomness it sounds like?
For the most part, genes do not change chromosomes. For example, for almost every human being on the planet gene OCA2 lies on chromosome 15. But the copying and combining of DNA that occurs for sexual reproduction is not perfect, and as Crash says, anything can happen. There no doubt are some human beings for whom the OCA2 gene does not lie chromosome 15, but genetic accidents like this shouldn't be of interest in an introductory course.
But let me ask: Is this swapping a rare occurrence or fairly common?
Gene swapping between chromosomes is rare. Extremely rare. The "jumping genes" that have been mentioned a couple times change location on a chromosome, not between chromosomes. Jumping between chromosomes is not impossible, but it doesn't happen very often. We can give the label Crashfrog's Law to the fact that things that are not impossible will happen at least occasionally.
Also, I'm assuming the DNA strand doesn't break for this exchange to take place, break apart and come together again, so it isn't exactly right to say that a whole GENE is being moved, is it? Is it right to say that whatever alleles are getting paired for particular genes are getting placed on the opposite chromosome or something like that?
This is a good question that involves the mechanics of protein production and the copying of reproduction. I'd be interested in the answer myself.