By Uditha Jayasinghe and Devjyot Ghoshal COLOMBO (Reuters) -Sri Lanka’s parliament will elect a new president on July 20, its speaker said on Monday, after protesters stormed the residences of the current president and prime minister, who have both offered to quit amid an economic meltdown. President Gotabaya Rajapaksa, who had overseen a ruthless crushing of the Tamil Tigers insurgents as defence secretary, is set to resign on Wednesday. His brothers and nephew earlier quit as ministers as Sri Lanka began running out of fuel, food and other essentials in the worst crisis since independence fr…