Baggage transfer on two separate tickets
 

Here's my situation:

Ticket 1: Air India (AI380): New Delhi to Singapore: Arrives in Singapore Terminal 2 at 7:20am
Ticket 2: Singapore Airlines (SQ16): Singapore to San Francisco: Departs from Singapore Terminal 3 at 9:25am

Total layover time is 2 hours. If Air India is delayed then I have even less time.

Option 1: I only take carry on luggage. Land in Singapore, take the sky train from T2 to T3 (takes about 5 min), go to the Transfer counter, get boarding pass, proceed to gate.

Option 2: Air India checks in my baggage all the way thru to San Francisco. I follow the same things as in Option 1,

Option 3: Air India only checks in my luggage to Singapore. I land in Singapore, clear immigration, claim baggage on T2, go to T3, go to airline counter to check in baggage and get boarding pass, go thru security, and then proceed to gate. This seems way too risky and almost a no-option.

What would you recommend?

Get an earlier flight to Singapore

And have VERY good travel insurance that will pay out if you miss the onward flight

Air India recently joined Singapore in the Star Alliance. You should be able to complete check in and bag check at your Delhiorigin.
I'd contact Singapore and ask what they suggest.

Option 2 is best. I've done this -- i.e. traveled on two separate tickets. At check-in, I asked the agent if he could check my bags all the way through, he said yes, and it was fine.