Hi fozziethebetta and welcome to the forum. To answer your questions, yes you should definitely get a heater. Bettas are tropical fish who like warm waters of about 78-80 degrees farenheit; anything colder and they tend to get lethargic. And keeping your light on for 8 hours is just fine, it simulates the natural light/dark cycle of a day.
For eating, well, your little guy is new to his home so he's going to take some time to settle in and get used to his surroundings. New bettas often don't eat during the first few days. However, there are a couple of things you can try. One is soaking his pellet in a little bit of tank water to make it softer for him. Another trick is soaking it in garlic juice (garlic powder with no salt dissolved in tank water works). Also, depending on how big he is, his pellets may be too big for his little mouth. You can try crushing them up into smaller pieces and see if he'll eat that way.
Give him a few days and if he hasn't eaten anything by then, you can post again and we'll try something else.
Oh, and be sure to post pics of your new guy.