the shifter may have a broken/weak return spring which is preventing the lever from returning to the centre when you shift down, hence why you have to put your foot right down and pull it back up.
also, strip it down and check your selector forks, bent/broken selector forks can cause all sorts of problems.
finding Neutral isnt always easy, on some bikes it will drop straight into neutral, on my DT i usually have to change into 2nd and then tap my foot on the lever to get it to drop into neutral, i've been told this is a worn detent plunger but it works so im not going to fiddle with it incase i break it
the crack wont have any effect on the engine compression and your lack of power is most likely the carb, if it isnt set up right i may be running the mixture overly rich (too much fuel, bogs down, no power) or too lean (less fuel, engine tends to run hotter and in extreme cases be low on power)
im not familiar with that particular bike but im assuming its a 2 stroke, if its a 4 stroke then check your vales and timing to make sure it is set up right.