Can a malfunctioning TPS cause an automatic transmission to have difficulty changing gears?

I have a 2000 Honda Civic EX, recently it hasn't been starting normally. I have to press the gas pedal after releasing the key and it will sputter to a start. There's a strong gasoline smell afterwards, and unspent fuel out of the exhaust. A coworker's husband is restoring a car (so I assume he knows... show more I have a 2000 Honda Civic EX, recently it hasn't been starting normally. I have to press the gas pedal after releasing the key and it will sputter to a start. There's a strong gasoline smell afterwards, and unspent fuel out of the exhaust. A coworker's husband is restoring a car (so I assume he knows what he's talking about) and helped me to try and diagnose the issue. He said I'm looking at either the TPS or the IAC.

When I got home I did some research and under the symptoms of a malfunctioning TPS it read

Difficulty changing gears
Poor fuel economy
Stalling at idle

I've been experiencing all of those recently, but I attributed the transmission issue to a malfunctioning transmission (sometimes* not always, my transmission will shift hard and it will shift from first into second, and "slip" immediately into 3rd, then it transitions into 4th perfectly. This doesn't happen always and there's no grinding noises, etc). I've been entertaining the idea that my transmission needs to be replaced, but if a malfunctioning TPS could cause that, then well that's a huge weight off my back.

Any and all information is greatly appreciated.
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