Welcome! Very interesting and adorable skink you have there

It's great to hear she can eat and is growing. I love her name too.
In regards to nail-clipping, you can try trimming before the lights come on, that way she's cool and can't put up as much of a fight. You can also add rough stones/tiles/flooring to her tank, or take her outside on something, to wear down her nails naturally. I like the natural method, but when I trim I just barely remove the tip usually. If you do trim and there's a bit of bleeding, don't panic, just keep it clean until the bleeding has stopped (as in don't put her back into the tank where dust/dirt could get into the spot).
Getting her to like you generally takes time and patience. You can consider finding things she likes and getting her to associate those with being with you. For example, if she likes fruits, consider taking her out and giving her fruits (there are mixed feelings about hand-feeding, so up to you). Once the skinks realize you're safe, and associate you with food/treats/explore-time, they generally calm down and even look forward to coming out. They also naturally calm down as they grow bigger.