I need to know what are the genes present on Y chromosome and what each is responsible for.

Then you'll be waiting a long time, because that data will not be available in completion until a great deal more research has been done.

Is it even that static?

Reasonably so, within species. There will of course be different alleles for some genes, which would be part and parcel of the whole description of the chromosome and its genes.

Apparently the Y is in danger of extinction (because it is an isolated subset of genes that don't normally undergo the 'random' exchange between pairs of chromosomes). I read an article in NS a couple years back, about what sort of replacement evolution might find for it (like hermaphrodites, say).

Gene map of the Y chromosome

 

There isn't a whole lot to the Y-chromosome. And since it doesn't go through recombination, I think the mapping may be more generalized. It can be long and it can be short. Looks like 53M making it the fifth shortest chromotin between the two from 20 and 21 respectively. X is 155M, so Y is missing 2/3rds of it's info. On the bright side of things: if it is lopped off like that, there is only one copy of the gene. Provided that copy is good, there should be no problem just using that. In fact it may be much easier with out all the winding and unwinding and the ungainly arm getting in the way. Which is why I reckon males are superior to females in most regards (or cretinous imbeciles).

Well, y chromosome DNA can be used in tracing paternal lines via ancestor DNA testing. Find out more here.