APune: Fastest and cheapest way to travel from Mumbai to Pune
My recommendation would be that you book a large taxi like Innova using a reliable cab company. Safe, reliable, fast and cheap.
ASingapore: Budget hotels for about 1 week close to Chinatown?
Try Albert Court Village Hotel, Village Hotel Bugis, Parkroyal on Beach Road for decent rooms. Alternatively, for cheaper options you could try Fragrance Hotel or Hotel 81....