Bettas are generally very hardy fish (as evidenced by their survival times in thos stupid little cups) but it will take a very long time to cycle a betta tank from new using a fishy cycle (2+months generally).
It's always better to use a cycled tank's media or a fishless pre-cycle.
Will he survive the cycle? Yes, but keep up on the ammonia/nitrite testing and do regular water changes. I'd say around 30% every 3rd day in your setup until it's cycled, at which point you can cut back to 1/week if you want.
As for lighting, so long as he gets a nice lights-off sleeping period of atleats a few hours a day at a regular time, they can be on or off as much as you like.