You did not mention the symptoms you are experiencing. But see the related link for how to check the fuel pump. To check the filter, you have to remove it.
fuel filter
The fuel filter is clogged and needs replaced. The second problem could be the fuel injectors are not pumping sufficient fuel to the engine.
Been there before. The problem will be in one of the fuel injectors.
The fuel filter on a 1989 Toyota Supra is located just below the fuel tank along the vehicle's frame. It is positioned inline and must be replaced periodically.
Already answered. It doesn't have one.
The "check engine" light is not solely dedicated to the air filter and pcv valve. There are other things that can cause this caution light to illuminate on the dashboard. Assuming you bought this car new and that it has but 37k miles on it, it's most likely still in warranty and Toyota should be fixing this problem for you.
have you replaced the fuel filter
I change mine every other oil change.
The problem may lie with a clogged fuel injector or a spark plug that isn't sparking.
If you replaced the oil filter, it takes 3.9 quarts. If you didn't replace the oil filter, it takes 3.7 quarts. As a mechanic, I would never recommend changing the oil without replacing the filter also. Toyota says you should use 5W-30.
You have to remove the transmission pan. Although it is only a screen and not so much a filter it should not ever have to be replaced unless the transmission has failed completely.
Yes , although you will have to top up the engine oil level ( or prefill the new engine oil filter ) * assuming you haven't put the required amount of oil in the engine already *