A New Toy

Nala is at the lake looking for a new toy. Sometimes she gets lucky and other dogs or dog owners leave their toys somewhere. Whenever she finds one of those it’s like birthday and Christmas combined! Will she get lucky today?

The grid is partially covered in fog. Entering correct digits will clear the fog from surrounding cells, possibly revealing more clues.

Normal Nurikabe rules apply for every box except box 5, which is neither "ice", nor "safe path"

Shade some cells (safe path) such that all shaded cells are orthogonally connected and no 2x2 is entirely shaded.

Every contiguous set of unshaded cells is ice. Each ice area has to contain exactly one circled cell. The circled digit indicates the size of that ice area. Iced areas cannot touch each other orthogonally, but may do so diagonally. Additionally, every iced area contains each number from 1 to its size (the circled digit) exactly once.

Normal sudoku rules apply. Place the digits 1-9 in every row, column and 3x3 box exactly once each.

Nala is curiously searching the safe path for exciting things. Digits on an arrow sum to the digit in that arrows circle. No 2 arrows overlap. All cells containing an arrow are always on the safe path and never on ice

Digits in cells that are connected by a white dot are consecutive. Digits in cells that are connected by a black dot are in a 1:2 ratio. Not all possible dots are given. (There is no negative constraint.)