As far as I can see from different texts, there seems to be no strict rule about putting comma after "Please" when it is used as an introduction to a request. Am I right?
In what cases using comma after "please" would be correct or even compulsory? What if "please" is put in the end of such sentence?
It is simply a matter of emphasis, which is why you can see it written both ways. For instance, if you had a visitor at your house, who was going to leave the house after you had left it, you might say:
Please don't forget to lock the door when you leave.
However, if this particular person had a habit of leaving the door unlocked, you would want to emphasize the "please", and could do it like so:
Please, don't forget to lock the door when you leave.
Which, when said out loud, has a louder "please" than the first example.
Basically, it emphasizes the importance of the request.
Also, if the "please" is at the end of a sentence, there must always be a comma, e.g.:
Don't forget to lock the door, please.