The extruder gear is the gear & motor assembly that pushes and pulls the filament. It is located on the left side of the X gantry (z rod goes up through the bracket that holds the motor). Everything relies on the extruder being accurate, and not having any slips or such. The stock pneumatic fittings (found at each end of the bowden tube) are low quality, and can allow the ptfe tubing to slip in and out. hence my comment about making a mark on the tube with sharpee near each end of the tube as an indicator, making it easier to see if the tubing slips. Slipping PTFE in turn means that if the motor is pushing say 50mm of filament through, but your tubing is slipping 5mm, then you're only pushing 45mm through. Sometimes the ptfe can slip all the way out, and then your not pushing any filament through the hot end, but instead pushing it all out the side of your printer (lol been there, done that).
If the gear is not tight enough, or if it's too tight and grinds down the filament, it can result in not pushing enough filament through. If the motor gets overheated, it can cause the gear to skip steps and not push enough filament through. There are lots of things that can cause underextrusion. Checking all the mechanical things means we don't have to try to band aid it by overcompensating in the slicer settings.
The layer shift you saw is likely caused by the belt skipping, or the bed/nozzle/something being obstructed partway through the print. There aren't any encoders, so the printer can never verify it's current position against anything beyond where it last was, and how much it was told to move. So if you bump the printer hard, it won't realize it, and will continue printing as if it hadn't been jostled or moved. The ender is a pretty tight kit, but double check your wiring to make sure it can't get caught or hung up on aything. ie the bed wiring catching on the y motor or something as the bed moves forward and back.
