Is compensation obligatory in the event of a small piece of a hotel room door falling off when it is opened forcefully, or when the latch of another room's door is damaged due to my pushing it open and then another person pushing it open?

If your opening of the door caused damage to something valuable, you are not liable for compensation, unless you transgressed in the manner of opening it. One should ignore obsessive thoughts (waswasah). The tenant is entrusted with the leased item and is not liable for it except in cases of transgression or negligence. Compensation falls directly on the one who caused the damage. In the second incident, compensation is on your companion who caused the damage if he transgressed in opening the door. Whoever is liable for compensation must seek absolution from the rights-holders by asking for forgiveness or paying the value of the damage. If it is impossible to reach them, then he must give charity equal to the value on their behalf.