Run diagonally (forward + strafe) for more speed. Level 2's totally linear, so there's not much else you can do to get through it faster.
All the keys on level 2 are plainly visible from the main path, it's just a matter of finding the path to them. Also none of them require teleporting, so if you spot the key and reach the teleporter for the next area before collecting it, turn back and keep looking.