How can I secure an outwardly opening front door without damaging anything?
For outward opening doors that need security against having the hinge pin removed, you can get hinges with a security stud in the hinge.



Sample image from Home Depot, no product or vendor affiliation

The small stud protruding between the middle screw holes prevents the door from being removed from the hinge while the door is closed.

You can create a similar result with a DIY solution by placing a long screw or lag bolt in the door frame that is left protruding almost 1/2" near each hinge. And on the door, drill a small hole to receive the screw head. It wouldn't hurt to cover that hole with a deadbolt strike plate to make it more difficult to force the door off and give it a more finished look.

These options are both on the hinge side of the door and have no need to install/remove as you use them. Most property owners wouldn't have a problem having something like this installed since you're securing their home.