If your drill will not operate some things to check are if the batteries are low or may be dead. If the batteries are not holding charge you may need to purchase a replacement battery. Also your brushes attached to the motor may be old or have dirt built up which can be replaced by following a replacement guide. The motor, which is the main source of power, may be burnt out. It can be replaced by following videos or replacement guides or the connections to the motor could simply just be dirty. So I recommend wiping down the connections and seeing if that helps.

If your chuck is wobbling first check to see if the chuck is loose, if so tighten it by turning it clockwise. If that isn't the issue than the threads that allow the chuck to tighten may be caked with build up not allowing the chuck to fully tighten, to fix this remove the chuck and clear any build up. If that does not fix the wobbling issue either than your chuck is most likely defective it is advised you purchase and install a new one.