Upvote:5
1) Probably 5-10 minutes walk, considering your luggage. The station is visible from the airport. There is a subway connecting to the airport to cross the highway.
2) More or less empty. Minimal traffic at the best. You can easily get a seat. The timetable for reference. You check the route from Tambaram to Chennai Beach to go to the railway station.
3) I don't know the cost, but not worth it. The seats probably have a bit of a cushion and that is it.
This is from when I used it maybe 6-7 years ago.