Karen, the only drawer we had on our Standard 13 was the silverware drawer. If it was pushed all the way in; it never opened on the road. If you meant the cabinet doors, that was a bit of a problem until I "pinched" the metal clips on the doors so they would hold tighter to the rollers on the cabinet. I used pliers and gently closed the clips a little at a time, until they were a little stiff to close. Same fix for the curtain rods if you find them falling off when under way.
door has a locking latch to keep it closed on the road as well. If you study it, you'll see it has two positions. If you close the frig door and swing the latch to hold it, it should stay shut. For storage, you can open the door a little and swing the latch in order to hold the door open to air it out and prevent mold. If the latch itself (ours was black) loosens, simply tighten it with a phillips screwdriver.
We always load the biggest, heaviest things on the floor and close to the axle
to prevent surprises when we check the trailer at gas or rest stops. Good luck with your new trailer. You will love it!