Kids run in hallways, the school has to deal with that.
Going outside without your permission is a whole different matter. If he does that immediately bring him back in. Give him a 5 min. timeout - chair in corner. Tell him if he doesn't ask that will always happen. Then ask him if he wants to go outside. If it is safe let him. Be consistent and swift. Don't threaten - do it. Don't take away liberties, do something immediately. Once you have that under control, move on the the next thing.
If he is hiding - and it is safe- then say fine, I had some cookies for you and quit looking for him. He is playing with you- and two can play that game.
My husband and I have been really struggling these past couple months with our 3 year old (almost 4 year old son). He is such a bright boy and much bigger for his age than he looks. We feel like we are at a dead end with how to handle the situation. We do the timeout, take things away, etc etc etc etc. NOTHING WORKS!!! The other day he even got up early and left the house without us knowing. We were floored! We told him dirty behavior needed a cleaning and made him clean up leaves from the yard...which he hated but it didn't correct anything. HELP!!! Where do we go from here? Is it just me? And for the record - no other siblings. Only thing that changed was he went from full time at daycare to part time in the summer and now back to full time. Could that be it???
I think that he is growing up and exploring. Nothing to do with daycare. Punishment done once usually doesn't work at this age (not a great memory for cause and effect). It will take a couple of times before it clicks. People talk about baby proofing there house, you need to do the same. He should not be able to get out the door when you are sleeping. If nothing else add a motion detector so you know when he leaves his room.
Also I would post to a new topic so others can contribute. I only looked at this because I was curious what you had to add to my prior post - always looking for good ideas.