Hi Subhra, Congratulations for getting a new member in your family.
I am not a veterinarian however I will try to answer the questions by my experience:
A1: The early sign of pregnance are shown at 28 days of mating, the abdomen may look a littlte heavy is the number of puppies are more than 3. Also there are pregnancy diagnosis kits which may be available with your local vet. Some vets suggest for ultra sound. The ultra sound may give exact results.
A2: I have always been breeding shepherds, the female rivalry thing can not have any definetive time period. One of my pair of females had tht rivalry for ever and unfortunately I had to gift one of them to someone else. however it is possible to dominate the more aggressive (as a master) one and try to neutralise the aggression.
A3: there are certain harmone (pheromones) which help males and females to lower the sexual aggression and make them rather calm with each other. I recently saw one such- "All OUT" type of device which fumes the kennel with pheromones to control such problems.
I hope this will help.