Given the fog that plagues DEL during the winter - you're generally much better of taking the 12:30 flight. And yes 1:50 minutes INT/DOM on separate tickets is hugely risky.

To answer your questions:
1. AI doesn't allow you to change tickets FoC for earlier flights the way United does. In this case *G doesn't help. Priority Standby is when a flight is fully booked - you'll get on top of that wait list if you opt for that flight - provided of course there aren't higher status pax than you (*G AI elites for example). Again I've used that a lot with United - I don't know if AI has the same kind of system - and I doubt they do. There have been a couple of times when I did arrive at the airport early and AI proactively offered me a currently departing flight (BOM - DEL sector of a BOM - DEL - USA flight) so maybe you could ask them when you land. It's nothing I would count on.

2. It's 4 hours not 3. When you leave the arrivals hall after customs - the domestic transit section is on your right (do not exit the airport terminal building) - if you're able to enter that area (people have had mixed reports about being able to enter >4 hours) you will be able to go through and enter airside at that point. Otherwise there's some seating in the area just outside the arrivals hall.

3. Yes of course you'll get lounge access. AI has a very ordinary lounge in DEL (unless the DEL airport lounge consolidation and upgrades are done by the time you arrive).