Congrats on your new girl, she's beautiful and I'm excited to see more LG keepers on here!
Erie is spot on here. Without a thermostat you're risking serious injuries to your new LG. I would say turn that thing off entirely until you get a thermostat to control it. You can pick one up at most pet stores, including the big box stores, but you can get an Inkbird or a Jumpstart, which I use, pretty cheap on Amazon. That hot spot is WAY too hot for a LG. I keep mine right at 88 degrees and he does wonderfully.
As far as tong feeding, I've always done it this way and haven't had any issues. As you've probably noticed already, they're pretty aggressive feeders and will smack their little noses on the thongs, so if you haven't already I'd pick up some rubber tipped tongs to keep them from hurting themselves. The ones linked below are similar to what I use, but you can get a cheaper pair.
https://www.chewy.com/zoo-med-angled...EaAiR2EALw_wcB
My guy use to eat mealworms, but overtime he lost interest in them. I think the movement of crickets and dubias just sparks his feeding response better, so don't get too worried if she won't take mealworms. Also mix it up a bit, don't feed the same feeders week after week, variety is the spice of life even for a little gecko.
As far as lighting, if your room gets a good bit of natural light, you don't NEED any supplemental light in the enclosure. I've kept LGs with light and without and both methods have worked. Now recently I upgrade my guy's tank and because of where I put it in my reptile room, I felt he could use some extra, so I'm using a small lamp, but for most of his life he's done fine with the window light.