Is the Y Chromosome unique in Homo sapiens?
No. Most mammals, and an assortment of other animals (including the often studied fruit fly
Drosophila) have the XY sex determination system. Some plants (such as ginkoes) determine sex this way.
There are other sex determination systems out there. For example, birds have a ZW system of chromosomal sex determination, where different chromosomes perform a similar function. There are a few animals (including some mammals) with an XO system, where females have two X chromosomes and males have just one, and Y chromosomes don't exist. There are lots of other variants too, such as animals where males and females have the same genetic complement and sex determination happens through environmental factors. (There are lizards where temperature performs this function.) I've even heard of animals where individuals are females during a portion of their lives, and males during other portions. Among ants and bees, unfertilized eggs become males and fertilized eggs females.
https://en.wikipedia.org/wiki/Sex-determination_system
Did the common ancestor had a Y chromosome .Do we know how many chromosome did the common ancestor had ?
The sex determination systems are an interesting problem for evolutionary biology. The different systems seem to be scattered seemingly randomly around the various taxa. The XY system is found in most mammals and it isn't hard to imagine that mammals share a common ancestral population if you go back far enough (probably before the dinosaurs) that we all inherited the XY system from. But if some insects and some plants also have the XY system, are we going to say that they are also descendants of the ancestral mammal population? Or vice-versa? And does the fact that some mammals don't use the XY system mean that they aren't really mammals at all and have a different ancestry?
Apparently there's a lot of convergent evolution taking place here. So is there some kind of pattern to it? Does evolution select for different sex determination systems in different circumstances? Do different systems confer different advantages?
There are some nice research topics for future biologists in all this.
At what point in time man started to have a Y chromosome ?
Probably long before human beings were human beings. We probably inherit the XY system from some Opossum-like ancestor that might predate the dinosaurs.
That doesn't necessarily mean that all animals with Y chromosomes have the same genes on those Y chromosomes. It's well known that genes (short segments of DNA) can move around and even jump from chromosome to chromosome.
https://en.wikipedia.org/wiki/Transposable_element