Any ideas for explaining a few strange things in a new house?

I'd start with the things that can be checked. A shelf of folded clothes can slide if it is tilted, wobbly, or bumped, and a door can swing when air pressure changes, even if the usual quick tests don't reproduce it. Check the door's hinges and latch, nearby vents, windows, and whether other doors moving changes the airflow.

For a week or two, write down when each event happens and what was running or open. A phone recording may help with sounds, but don't set up anything that could create a hazard. One failed attempt to recreate an event doesn't rule out a cause that depends on specific conditions.

The bed-patting detail could be worth separating from the house noises. Brief touch sensations can happen as someone is waking from sleep, and can feel very real without showing that anything touched the bed. That possibility doesn't explain the door or the sweaters, so I'd look at those separately rather than forcing every event into one explanation.

Also make sure smoke and carbon monoxide alarms are working. If anyone in the home has headaches, dizziness, confusion, or other unusual symptoms, leave and get the home checked promptly. Those symptoms don't prove a cause, but they are a reason to take safety seriously.

Unexplained is a fair description, but it isn't the same as evidence of a haunting. I'd check the practical possibilities first and avoid telling a young child that floating lights mean something is in the room. Ask calmly what they notice, without suggesting an answer, and see whether there is a repeatable pattern.

If the checks turn up nothing, it's okay to leave the events unresolved for now. You don't have to decide on a paranormal explanation just because one incident hasn't been recreated.