I think your type 2 queries might be $$$\mathcal O(\log^2 n \log y)$$$.

while (pos <= n): This while loop executes $$$\log y$$$ times, once for each continuous segment.

first_small(pos,y), Get_pos(pos,y): Both of these seem to be $$$\log^2 n$$$ operations. They each have a $$$\log n$$$ while loop and call Get(1,1,n,pos,m) or Get(1,1,n,m,m) at each iteration, which is another $$$\log n$$$ operation.

To remedy this, replace Get(1,1,n,pos,m) or Get(1,1,n,m,m) by simply checking the sum of the subtrees in $$$\mathcal O(1)$$$ when deciding which children to traverse to.