You can clean and grease the DS cup from the NDS, once you've pulled both cranks and the spindle. If there's any pitting in the cup (which can be felt with a ball point pen), you'll need to replace it. If it's hard to wrench out (stress on the left hand threads), tap the wrench handle with a mallet. Use a heat gun if needed. This can be the most difficult overhaul job on some bikes.
Good catch, finding the loose crank arm. You wouldn't want to ride it that loose.
Be sure the threads in the crank arm for the puller are clean, and that the tool is bottomed all the way in. Use light torque on a crescent wrench to be sure. That can be a difficult pull, too.