I haven't kept northern blue tongues in my personal collection, but I have worked with them!
Yes, topsoil and play sand works great! It's the base for my bioactive arid mix. Depending on your house's ambient humidity, you may need to add some sphagnum moss. I like adding orchid or coconut bark for aeration too, especially if the the ratio of sand is above 40%, but I've had success without it.
This is the lighting chart I've used in the past both personally and professionally for these guys and reptiles with similar requirements. It's from Arcadia Reptile.
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It's hard for me to give exact recommendations. I'll always recommend T5 bulbs since they have newer technology and are safer/more reliable. The Zoo Med 5.0 and 10.0 are pretty much interchangeable with the Arcadia 6% and 10% respectively. They should be able to escape direct exposure from UVB, so aim for a bulb that's 2/3s the length of the enclosure. I don't know if you're looking for heating suggestions, but I love halogen flood lamps. Depending on the distance between the top of the enclosure and your basking spot+ your ambient house temp, I'd say something like a 50 or 80 watts should be good. I'm not the biggest fan of heating pads, especially for diurnal reptiles. I love a rock or slate tiles for their basking spot so they can get belly heat too.
Since your skink with have exposure to UVB, they'll be able to synthesize pretty much all the D3 they need. So I'd dust with without D3 most of the time, with vitamin with d3 monthly. If you were concerned though, it wouldn't harm anything to dust with d3 monthly as well. I don't know about baby juvenile skinks, but I feed an adult twice a week, but I know some skink keepers feed weekly.
As far as plants go, skinks tend to burrow so they may be dug up. If you plant the plants in pots and then bury them, you may be able to make it work. Aloe vera is my favorite plant for arid tanks. I'd definitely recommend adding bark chips for soil creation if you decide to use live plants. You can add horticulture charcoal or worm castings in your soil mix to support plant health if you want to, but it's not necessary (like 5% each).
Ceramic heat emitters are a great way to add extra heat without light (you can use them at night too!). You can find them at wattages as low as 25.
I don't have experience with sweaters or vests for reptiles so I can't say. But I can say that since they are cold-blooded they might slow down how fast they lose heat, but they aren't going to keep them warm the same way a mammal would. But I take my reptiles out when temps are 70-80 F.
I hope this helps! This care guide pretty much aligns with what I was taught in regards to nbt skink care:
https://reptifiles.com/blue-tongue-skink-care/