I own Suzuki swift diesel. When I start the car in morning for the first time in day, the engine oil light stays on for 4-5 seconds after engine has started and then goes off and never comes back again. Additionally if I restart after 5-10 mins it stays on for about 1 second after start. Also I have changed the engine oil yesterday and it has happened only twice or thrice. How much damage would this had caused by now ?
There's usually no wizardry around the oil light. It's a pressure switch. If there isn't enough oil pressure to "tip" the switch, your oil light will appear.
Recheck your work around the oil change. Fluid refill level and oil leaks at the filter.
Others will chime in with paranoia, but you're almost certainly fine if you haven't been idling the car for long periods or loading the engine. I've seen first hand how long an engine can last with little to no oil- much longer than you'd think.