Toyota Corolla 89 Losing Power/Fuel Smell

My relative's mechanic is out of town for a while, and I know very little about the maintenance of this hand me down manual shift car, but
recently, it's been losing power to the point that it's almost undrivable. (And it's not a Turbo car). It starts off ok for a few blocks, but as you have to stop and start, at stop signs, etc., then it really lags. And if you try to take it on an open road and can get it into 3rd or 4th, the fastest it will go is ~30-40 kmh in those gears (and of course, it will shortly start to shudder due to lack of speed per gear). And all that's with the gas peddle to the floor in each gear.
The car did have a catalytic convertor repair a few months ago (I think he replaced it for the Drive Clean checkup), and I am wondering if this could be it (?) because a few weeks ago, strange, long fibreglass black hair started coming out the exhaust pipe. I pulled around 4 chunks of it out over a 2 week period. (It looked like a silky squirrels tail).
I've checked all the basic things that I can: the spark plugs (one was a bit wet, the other 3 bone dry and pretty clean), the air filter (a bit off white, but nothing dire), fuel filter, checked the oil (also a bit dirty, but still topped up).
I'm assuming the car is flooding because I can smell raw gas when I start it up. However, there is no leaking trail left behind as it drives away and no oil leaks left where it's parked. I did notice a vibrating sound earlier in the week, coming from either the exhaust or muffler area, a few days before the car started losing power. I thought maybe the muffler was going, but now I see that the sound was just from pushing the gas pedal all the way down and getting alot of noise, but very little power. Anyone have any ideas on what could be going on here? Thanks for any input.
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Sounds like you exhaust may be restricted, either the cat broke up is breaking up and pieces are caught in the muffler.

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part of your trouble sounds like a fuel leak under the hood.
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Sure sounds like an exhaust restriction problem. Which may be secondary to what is causing the cats to not drive clean in the first place, like an emissions problem? Incorrect cat. used in replacement? A scan may show the culprit. (Just gotta ask this: Otherwise, what color hair did Jimmy Hoffa have?) Luck to finding why the exhaust is getting restricted. s
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