I have a few querstions about timing, Specifically when powers are declared and when characters take damage.

1.) If I use HSS, do I need to finish my movement before the damage is taken and the dial is turned?

2.) For the GCPD Cruiser, Do I need to place the damaged figure before the dial is turned when using clear the streets?

3.) Can I wait for my opponent to decide to roll BCF or do I need to declare my use of Probability control before they decide to roll the d6?

1) They take their damage, then continue your movement.

2) IDK

3) If you wait till after the BFC rolled that will be the roll that gets rerolled

1) They take damage normally, then you continue moving.

2) As soon as the Cruiser enters a square with an opposing character you move that character then deal them the damage and then finish the movement of the Cruiser.

3) If you want them to reroll the attack itself, then you need to PC before the BCF roll. If you wait, then you're PC'ing the BCF roll itself.

I understand that, what I want to know is, am I allowed to ask if they are going to roll for blades before deciding to prob the attack? Can my opponent make his decision to roll for blades based on my decision to prob the attack or not?

No. BCF is rolled when the attack is successful and you're moving to the damage dealing portion of the attack. The attack is not considered successful until both players acknowledge that it is due to effects like PC.

Yep.

If you ask me if I'm going to roll Blades or not, I'll just say "It depends on if the attack hits".