Are you providing any force when your partner is punching? I learned to kind of "catch" punches with the mitts to ensure that my arm isn't getting whipped back unnaturally, and to ensure that the puncher has a solid target to hit. The amount of force you supply is related to how hard they're hitting.
2. My right elbow gets really sore after holding for a while - it feels like a tendon or something is getting sprained, and it can be pretty intense. Seems to happen when I hold for a really hard right cross or right hook, and it just keeps "accumulating" in terms of pain level. Am I holding wrong? I usually hold around shoulder level for the guy striking, and typically the mitt is slightly to the right of my right shoulder, like if you were waiting for a high-five. This has been a recurring problem. In the past, I thought it was due to not being fit enough, but despite massive improvements in muscle mass in my arms, I still have the same problem.