2007 Toyota Corolla engine vibration, low milage

You can't identify a defective part this way. The place to start is by having the diagnostic fault codes read and recorded. An engine vibration is usually due to a misfire, and some fault codes will identify which cylinder is responsible. The first suspect would be spark plugs that need to be replaced.

When you have a misfire due to a spark plug issue, unburned fuel and air will go into the exhaust system where the oxygen sensor will detect the unburned oxygen and the Engine Computer will interpret that as a too-lean condition. In response, the computer adds fuel, but it adds it to all the cylinders. The exception could be that since a misfire has been detected, the computer may be altering the fuel metering calculations as a result, because this number:

long term fuel trim -; -20.3%

is the opposite of what would be expected. Minus 20 percent normally means the computer is commanding 20 percent less fuel than what is considered normal. 20 percent is a REAL lot. Normal readings are around plus or minus two or three percent.

The fuel mixture is supposed to switch between too rich and too lean about two times per second. That is needed to make the catalytic converter work properly. It is likely the exhaust is never going into a lean condition because of all that unburned fuel from the misfiring cylinder, and that's why the computer is continually trying to reduce the amount of fuel. No matter how much it cuts back on fuel, the exhaust will never go into a lean condition, so the computer keeps reducing the fuel more and more without success.

Rather than trying to interpret these numbers in a useful way, approach an engine misfire like you would on any engine. Start with the basics first, like spark plugs, then ignition coils.