To add to the existing answer:
- What is the connection of getting rabies from a dog and his death?
An observation period of 10 days is one way of determining whether an asymptomatic, low risk animal has rabies. Domestic pets are lower risk than wild animals, although this is a stray which puts this pup at risk. Biopsies from the brain (post mortem) is the only definitive way to diagnose rabies.
- Should I be worried if he dies within a week?
Dogs are in a lower risk group of carrying rabies, but it would be worrying, although there could be many reasons for the dog's death. I think observing the dogs health prior to death would also be a good idea. If the dog had trouble walking, swallowing, produced excess saliva, wouldn't drink, became excessively aggressive or shy (although some of these are also symptoms of other conditions).
- Does bite from a 2 months old puppy can risk humans being infected
Yes if the dog has rabies, the skin is broken and saliva comes into contact with the wound. In fact people with open wounds should take care when handling things that may have been rummaged by rabid animals, as the saliva can still transmit the illness through an existing wound, the animal doesn't need to bite the person. The same can happen through the nose and eyes.
Rabies is spread by saliva and brain and nerve tissue.
In terms of minimising the risk washing and rinsing the wound well in soapy water is the first course of action.
If rabies has been transmitted, waiting to see if the dog dies is too late for treatment of the human being if it is indeed infected. By the time an individual (any type of animal) is displaying symptoms, the disease is usually fatal, so time is of the essence.
In the United States, postexposure prophylaxis consists of a regimen
of one dose of immune globulin and four doses of rabies vaccine over a
14-day period. Rabies immune globulin and the first dose of rabies
vaccine should be given by your health care provider as soon as
possible after exposure. Additional doses or rabies vaccine should be
given on days 3, 7, and 14 after the first vaccination. Current
vaccines are relatively painless and are given in your arm, like a flu
or tetanus vaccine.
Centers for Disease Control and Prevention, Rabies, When should I seek medical attention?
Human rabies immune globulin (HRIG) is administered only once, at the
beginning of anti-rabies prophylaxis, to previously unvaccinated
persons. This will provide immediate antibodies until the body can
respond to the vaccine by actively producing antibodies of its own. If
possible, the full dose of HRIG should be thoroughly infiltrated in
the area around and into the wounds. Any remaining volume should be
injected intramuscularly at a site distant from vaccine
Centers for Disease Control and Prevention, Rabies, Human Rabies Immune Globulin
General reference for this answer: Centers for Disease Control and Prevention, Rabies