I have a Merauke and I don't think that is what you have. It may be an Irian Jaya but definitely not a Northern. I suggest you show these pics to the keepers over at bluetongueskink forums. They have a mountain of info for each species and subspecies as well as a number of breeders who can confirm this for you.
Nonetheless, T5 is too strong for blueys. A T8 is more suitable or make sure to raise the T5 fixture higher than 12" from your lizard. Blueys are not like beardies and while this is in debate, many don't even use UVB for their lizards. I would do it anyway but elevate your T5 or exchange for T8. Then a Reptisun 10.0 bulb for the T5 or T8 will work.
Since it is not a Northern, you are working with a humidity required species. Some blueys prefer to burrow over using hides so provide about 3 inches of substrate like coco fiber and see what it does. These are creatures of habit so if it burrow, that is what it will always prefer to do. Humidity should no less than 50-60% at all times.
Blueys do best in enclosures with plenty of floor space. I recommend no less than 48" long and no tubs for these guys.
I don't use t-stats on my lizards. Lizards in general know how much heat they want and when to move away. It does not hurt to have it if you already ordered it. Blueys in general sleeps a lot and bask for a few hours in between if they are not exploring.
About the toes, do your best to remove the stuck shed. The humidity you are going to provide will help immensely.
Make sure you have your calcium plus D3 supplements and multi vitamin. As an adult bluey, they only need to eat once a week or no more than 2x a week depending on his health.