2004 Chevy cavalier - car is "bucking" or "jerking" sometimes at acceleration, and other times at cruising speeds (40-50 mph)?

When it does happen, (not every time I drive) sometimes its just one or two jerks, other times its 3 or 4 (this happens more at lower speeds) No other glaring symptoms, but this is a cheap "get me where i need to go" vehicle so I just need to keep it running without spending tons of money hopefully. Here... show more When it does happen, (not every time I drive) sometimes its just one or two jerks, other times its 3 or 4 (this happens more at lower speeds) No other glaring symptoms, but this is a cheap "get me where i need to go" vehicle so I just need to keep it running without spending tons of money hopefully. Here are a few things that may or may not be noteworthy in diagnosing this issue...

I lost the fuel cap about a month ago and haven t replaced it yet.... πŸ˜•

It leaks oil like a b*tch, so I m constantly putting oil in it (bad seal on oil pan)

The gas gauge doesn t read if it gets lower than a quarter of a tank which has caused me to run out of gas on a few occasions.... which I know can be rough on the pump and injectors, so i try to put fuel system cleaner in it every so often

The check engine light started popping on randomly a few months ago, but now stays on constantly since i lost the fuel cap. BUT the kicker is I cannot read codes on it, because the douche nozzle that had the car before me tore the dash out to install a stereo, and somehow hid (I m assuming, haven t took it apart to look) the connector for the code reader when he put it back together

I believe the lower engine torque mount needs replaced (this was suggested to be part of the problem by a friend, and after inspecting all 3 motor mounts, that one seems to be loose
Update: **Edit** incase it isn't obvious... I need advice on what could be causing the jerking, and how to fix it
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