Do I need a Singapore transit visa?

Looks like the rules have since changed since 2017 (or correct me if I am mistaken as I am travelling on a round trip via Singapore later this year). As given here in the ICA's link, the rules for Indian nationals stands as follows.

To be eligible for a 96-hour VFTF an Indian national must,

1. Enter Singapore by any mode of transport but depart only via air or sea. You must have a valid onward air/ferry/cruise ticket departing Singapore within 96 hours; and
2. Have a valid visa/long-term pass (with a validity of at least 1 month from the date of entry into Singapore under the VFTF) issued by any of the following countries:
   • Australia
   • Canada
   • Germany
   • Japan
   • New Zealand
   • Switzerland
   • United Kingdom
   • The United States of America

In the above list, the visas issued by Germany and Switzerland applies to visas issued by Germany or Switzerland or Schengen visas that are good for entry to Germany or Switzerland.

A visa is considered valid so long as it is good for entry into one of the eight countries listed above. Travellers with Single Journey Visas (SJV) may still be granted VFTF on the return leg of their journey (i.e. after the SJV is used and no longer valid), but you must:

• Travel directly from the country that issued the SJV, en route through Singapore, back to your home country
• Not have returned to your home country since you last used the SJV.

So it appears to me that Indians with a valid USA F1 visa can use VFTF on both legs of their journey.

As your itinerary takes you through Singapore on both legs of your journey, you would need a multiple entry visa.

The Singapore Immigration & Checkpoints Authority (ICA) information on the Visa Free Transit Facility (VFTF) is explicit that, for Indian nationals, it is only only valid for one transit in the itinerary, either forward or return leg, but not both.

Travellers who are nationals of India

Indian nationals who are in transit to or from any third country by air, may be eligible for the 96-hour VFTF for one transit in the itinerary (either forward or return leg, but not both) if they:

1. have a valid onward air ticket departing within the next 96-hours; and
2. possess a valid visa/long-term pass (with a validity of at least 1 month from the date of entry into Singapore under the VFTF) issued by any of the following countries: Australia, Canada, Japan, New Zealand, United Kingdom, United States of America, Germany, Switzerland

A visa is considered valid if it is not expired and is good for entry into the third country.

The VFTF for Indian nationals is for air to air travel only, and is only valid for one transit in the itinerary (either forward or return leg, but not both).

Single Journey Visas (SJV) issued by the above countries are also acceptable when transiting through Singapore on the onward or return leg of the same journey. For those on the return leg of the journey, i.e. after the SJV has been utilised, the following conditions must be met:

1. The traveller travels directly from the country that issued the SJV, on route through Singapore, directly back to the home country; and
2. The traveller has not returned to their home country since the SJV was last utilised.

As stated in Timatic, the database used by airlines:

Visa required, except for Nationals of India who can also transit, for up to 96 hours without a visa under the Visa Free Transit Facility (VFTF) on either the outbound or return leg of the same journey (but not on both). Leaving the transit area is allowed.

So no, you cannot leave the airport on both journeys, only one.