Rhythmic knocking/pumping? noise from back of 05 cavalier

First, let me apologize in advance. I really don't know anything about cars other than the little I picked up from repairs I've had done on mine. Almost 2 months ago I bought an '05 cavalier from a used car dealer. Had a LOT of mileage (94,712) but seemed alright. Turns out it was a lemon. I got it "as is" so I've had to deal with it. Since I've bought it I've had to replace 3 bearings, a rim, a tire, the stabilizing bar (??), a cv joint seal, the transmission pan and gasket, the alternator, two sensors (oxygen and...temperature something..), some hose that hooks up to the regulator (I think?), the fuel filter and the fuel pump, 3 springs (not sure what those are) and an adjuster (or that..it's on my receipt though). I may actually be forgetting stuff. I'm pretty sure my mechanic has almost entirely rebuilt my car. A lot of the parts he bought were used but he said he checked them out to the best of his ability. It seems to be running fine for the most part.

All that being said...when I brake and accelerate there's a funny noise. It comes from the back of the car and I really only notice it after I've been driving for awhile, mostly at stop signs and lights. It's very rhythmic. Almost sounds like a pogo stick or something, but a little less springy and a little more knock/thump. I actually thought it was the stuff in my trunk at first but..I'm not that lucky. Any idea what it could be? The mechanic did tell me that I'm probably going to have to replace the discs. I'm not entirely sure what those are or if that's relevant but to my knowledge that's the only problem that still exists, although he made it sound like it wasn't one that required immediate attention.

Well "M" this does sound like a dude for sure. Welcome to AF. Did the "mechanic" say anything about the rear struts/shocks and rear strut mounts. From what You are describing it could very well be that problem. not sure what he meant by discs other than rear brake drums. How are the brakes when you apply them ? are they noisy ,do they grab hard almost putting You thru the windsheild or do they seem normal? one other thing ,I`ll assume that the muffler is tight and not knocking ..........correct? What rim and tire was replaced, was the tire worn on the inside or outside or just generally wore out due too high mileage? Hope You didn`t pay much for this car

No..he didn't mention any of that. And I have no idea about the muffler lol. How do I even check for that? The brakes seem okay except the car kind of rocks back and forth when I'm stopped. I definitely paid too much for this car. Buuuut Texas has a DTPA law and I'm gonna try to file a lawsuit. The car was in an* accident and I think maybe even had flood damage and they didn't let me know.. The back driver side tire & rim was replaced. The rim was all bent, I guess from the accident, and the car lot actually put weights on it to try and even it out. One more quick question..the car has an in tank fuel pump. It's got a lot of wires and stuff and the people who sold it to me rigged it or something. The top part of the pump doesn't match the bottom part and you can see where they melted some little..tubes..or something..to get them to fit together. They also spliced some wires and the guy who was fixing my car said that's really dangerous. Makes sense to me, but I googled it and it actually seems pretty common. Any idea? If it's as dangerous as he made it sound that's one more thing I'm gonna hold against the dealer. I have all of the original parts and pics of some of them still in my car.

Have your "mechanic" look closer at the driver side back wheel to see if anything is bent internally, hub/bearing assembly. This could be the source of your noise. the strut mounts cannot be checked till the struts come out. if you can get somr beefy to try and rock the rear of car up and down ,you MAY get some noise from bad struts/mounts. As for the muffler what I meant was it is tight and not flopping around. Can`t help you with your other question........sorry. Good luck