Will I have to eat foods only on my right side for 3 months when 2 lower left back teeth are first bone grafted prior to dental implants?

For the most part! A major key to success in a bone grafting procedure is to leave the area undisturbed during the initial phase of healing when the blood supply to the graft is developing. As the graft becomes more integrated with your body, you'll be able to function more in that area. Be sure to follow your doctor's instruction exactly for eating and for hygiene. .
Not typically. Sometimes you will find you have to chew predmoinantly on one side simply because you are missing teeth, but most grafts are comfortable enough to be able to chew after just a few weeks.
Soft diet 2 weeks. is recommended only for 7-10 days. Then avoid hard, crumbly, particulate foods (e.g. popcorn, peanuts, crust, rice, corn, peas, raisins, etc.). Eat other food carefully to protect the bone graft site, for approximately four weeks. Good luck.