Unsweetened applesauce is used to decrease the amount of butter in the recipe. If you don't want to use applesauce you can use ⅓ cup of melted butter (total).
For the sweetener, you can also use pure maple syrup or honey if you wish.
Paper liners will usually stick to these muffins since the batter is low in fat or has a high protein content. I recommend you forego liners if you want an optimal experience.
If you are using paper liners, use high-quality liners. Invest in good-quality, non-stick paper liners. Cheap liners are more likely to stick. It has happened to me. You can also grease the liners. Lightly spray the inside of each paper liner with non-stick cooking spray or brush with a little melted butter or oil. This will create a barrier that helps prevent sticking.
If you are set on using liners silicone liners will likely work the best. These are non-stick and reusable.
If the liners are still sticking, try refrigerating or freezing the muffins for a short time. The cold temperature can help the liners peel off more cleanly.