It should heal fine. Assuming your immune function is normal, this should not be a cause for alarm. Any time there is a cut, you should try to clean the area, (water works the best for minor cuts at home). Then pat the area dry and if needed cover with a bandaid. Watch the area for redness surrounding the cut, or any puss like discharge from the wound. If you think there is an infection, see a physician.
Should be fine. Use a topical antibiotic such as bacitracin.