Solution

163695

First name
Liam
School
Furness Academy
Country
Age
0

I think that it is only possible to select 10 blue spots without making a square. I think this because if i highlighted any of the other spots then it would form a square on its side or flat.

I worked this out by selecting all 16 blue spots then using process of elimination to make sure there are no squares in this 4 by 4 grid.