In the "what are you doing today" thread,
@MickaC mentioned unsweetened applesauce as a substitute in baking. I often use it in muffins or cakes for half (or more) of the oil or eggs and cut down the sugar accordingly.
For eggs substitute, sometimes I use half ground flaxseed and water and half applesauce.
Love Aldi's unsweetened applesauce, but wound up throwing away too many half-filled jars from spoilage because I didn't use it fast enough. These days, after opening a fresh jar I split the remaining applesauce into one cup (ish) sized portions. Keep one in the fridge and freeze the rest in small plastic containers or freezer bags laid flat.