Hey, welcome!
I'm somewhat of a new owner as well, but i've asked so many questions and have figured out the best way to deal w/ these things..
When i first had mine, I didn't see them eat at all for a day or two, but in fact they had eaten at night. Sometimes they just won't eat at all for a day or two, or they'll go crazy and stuff themselves. I've found that they eat a lot more in the evening/during the night (if i leave a bowl of mealworms for them to snack on). However, I try to provide food all of the time of the day. For instance, when i wake up, before going to school i'll make sure there are about 9 mealworms in a bowl for them (i have 3 geckos, they're probably about 2 months old). When i get home, I'll put crickets and mealworms in the tank and try and get them to eat them by letting them roam around and by placing food in front of them. I've even gotten them to eat out of my hand which is pretty cool considering how young they are. After time it seems that your geckos may become accustomed to certain times of the day that you will feed them. So like if you bring them food at 6 every night, they'll eventually learn this and expect it. My guys eat ALL THE TIME. Since they're young, try to get them to eat as much as possible.
I use a UTH (under tank heater/heat pad). It doesn't mess with the day/night cycle because it doesn't provide any light. However, my geckos are active during both day and night. They are usually the most active in the late evening (after 7 or 8 PM).
As far as calcium goes, I try to dust the crickets/mealworms as much as i can, but i also keep a bowl of calcium in the tank, to ensure that my leos get as much as they need. Everyone suggests using Calcium without Vitamin D3, because, even though vitamin d is essential for calcium to be effective, leopard geckos are naturally nocturnal, so they don't receive much if any D3 from the sun, so they don't need it. Also, I've heard that too much can be toxic and can kill them
.
-----
0.0.3 Leopard Geckos
0.1.0 Miniature long-haired dachsund