Answer:
Convincing the people to shift the capital would be pretty easy. I would advice the sultan to presented the idea through military point of view. Daultabad were located on higher elevation than Delhi. Which means that in case an attack happened to the capital, the military will have high ground to fight from as an advantage.
Convincing the people to change currencies would be more difficult.
Traders, craftsmen, artisans, and performers built the current economy using the old currency. Changing it right away will caused a disruption in the economy. I would advice the sultan to order a slow transition. Meaning that he need to pass a law that enable the use of both old and new currencies for a couple of years. This will help the people getting used to the new currencies before we eventually stop its usage in the future.