I hold Indian Passport and Green Card from US (Permanent Resident), will be transiting from India to US via SIN airport. Have really long layover (16 hours) and want to enjoy time in City than staying in SQ The Private Room.

1. Do I get this 96 hours transit visa after arriving at airport OR this is something I need to plan ahead?
2. If I get after arriving, is there any process?
3. I'm really interested in City Sight Tour (free tour offered by Changi Airport) or maybe even stay 1 or 2-night/s in Singapore.

Any help is appreciated before I change my flight accordingly specially if I plan to stay night in City.