Do you leave the door secured all night or do you remove it after child falls asleep?

This is really up to you. 

If you want to allow your child to use their exit limit for each overnight wake up, then remove any door lock once they fall asleep.

If you want to secure the door for the entire night after they exceed their limits, you can leave it secured. 

Remember, this process is not meant to last forever. This is a temporary situation for long-term gain.
For safety, your child's door should be unlocked overnight.