On separate tickets it is completely crazy. As far as 9W is concerned, you are a local passenger, and so if you miss your flight, it's your responsibility for not getting out of bed on time. 75 min is very tight in any case, but when there are separate tickets, 6 hours or more is advisable. It's not just a matter of DEL airport; international flights being late by an hour or so because of departure delays is not uncommon and hardly counts as a significant delay.

Transfer passengers are rare and I am not sure if luggage can be interlined, plus some airlines do not interline if you have separate tickets (unless both airlines are in the same alliance). I don't know about LH/9W specifically.

Yes, DEL has fog in January, and late night / early morning are the worst times for fog. Your arrival flight is more likely to be affected than your departure flight.

Better to stay in DEL for a day, you probably haven't seen everything or eaten in every good restaurant.