Proper shoes . Heel pain is commonly due to plantar fasciitis. Best strategies are well fitting, supportive, well cushioned shoes with a good arch. It often helps to use a silicone heel cup. A regular stretching regimen is important to focus on heel cord stretches and plantar fascia stretches. Finally, consider cross training by waking some days, and bicycling, swimming, elliptical on other days.
Depends. If you are having so much pain that you limb than yes, you need a week of rest. However, if you are not limping than you can continue walking but do a lot of stretching of your calf muscles and make sure your shoes are supportive running shoes. You may also try an otc superfeet inserts. You may ice and take anti-inflammatories as well. If not better than seek foot doctor.