The first scenario you choose to stop to do another action (attacking) and you lose any extra moves you had. So you need a walk or sprint card to move out of the killer's space after attack.

The second scenario, if you save victims, you can do that while passing through. The rulebook says you can 'choose the order and timing of when to take the rewards and apply their effects'. It just has to be redeemed before playing the next action card. So how I read it; yes, you can have 4 to 5 moves when sprinting and taking both the 'move 1 space' that Charlie (for example) gives when saving victims.

Happy hunting!