Short answers, pulled from the story.
Sawai Jai Singh II ascended the throne of Amber at the age of eleven. He inherited a kingdom that was financially depleted and could barely afford to maintain a cavalry force of one thousand men.
Sawai Jai Singh II earned the title Sawai after his feat of arms at the siege of Khelna Fort in 1702. This title means one and a quarter times superior to his contemporaries and declared his exceptional capability.
Sawai Jai Singh II built five astronomical observatories at Delhi, Mathura, Benares, Ujjain, and his own capital of Jaipur. These structures, collectively termed Jantar Mantar, include instruments like the Samrat Yantra and the Ram Yantra.
Sawai Jai Singh II officially replaced Amber as the capital of the Kachwahas by 1733. Construction of the new capital began as early as 1725, and the foundation stone was ceremonially laid in 1727.
Sawai Jai Singh II performed ancient Vedic ceremonies like the Ashwamedha sacrifices in 1716 and the Vajapeya in 1734. He also promoted the abolition of the jaziya tax in 1720 and the reduction of wasteful expenditures associated with Rajput weddings.