RPM's dropping and bucking when driving over bumps

So i've been going through this aggravating thing for months now and its becoming quite unbearable.
Ever since i disconnected my battery to change my spark plugs with NGK Iridium 6510 plugs on my 2010 Ms3, it bucks and jerks rather violently when i hit bumps and uneven pavement. It also does it when i make sharp right turns. Months ago i cleaned my throttle body and it stopped the issue for about a month, but now its back.... I've tugged and wiggled any and all wires i could see from the top side and the bottom side and nothing caused the engine to almost die (short version)

the problem started to come back, so i was like "oh let me clean the throttle body again" only because that's what seemed to work last time. I cleaned it, with the battery disconnected once again, and put everything back together the exact way it was. I read something online about an "idle relearn" procedure and i decided to go ahead and follow that. The method was to let the car idle for 15 min with no AC or any other systems running. Then after that period, let it idle for another 15 min with the AC on full blast. HOWEVER before i even got to the second 15 min period, the engine shut off. I tried to start it back up and it would crank, but wouldnt start. I had to let the car sit for about 20-30 min before i could start it again. After i got it started again, i decided i just needed to move the car from the garage and go park it down the street where i normally do, and the second i started to drive to my spot ( 100 ft away ) the engine shut off and i was in the same scenario as before...cranked but wouldnt start.
The car did this for about 2 weeks, i couldnt drive it at all. I kept disconnecting the battery to try and re-do the relearn procedure, but it never helped.

Fast forward to the third week, i was able to get my dad to come help me figure it out. Long story short we had to keep giving the car throttle any time it was about to die... like i mean he had to SPAM the gas pedal with his foot for a solid 5-10 min for the car to stay running. And after a certain point it finally just died. However we were able to get it started back up with the next turn off the key, just for it to die again.
Once we finally got it to run by itself after multiple attempts, we got out of the car, and i closed my door and the engine almost died. Any sudden movements of the car would cause the rpms to drop and the engine would almost die. Weird right?
Anyway i got in and drove it around the parking lot, and it was ROUGH! Rpms going bonkers and the car obviously bucking like crazy. As i was driving it though it was getting better and better.
Eventually i was able to drive it home ( 10 min away ) with it not shutting off at all. It did buck though.

Where im at now is the car drives and works, but im back to square one. The car bucks bad when i make a sharp right turn, and it bucks when driving over bumps. Im thinking its electrical, but ive tugged and wiggled every wire i can see on the bottom of the car and on the topside, and i never got any rpm drops. I brought it to the mazda dealership and they didnt tell me much other than to buy the OEM airbox to see if that helps, and to have some compression tests done. They also disconnected the topside 02 sensor and nothing changed. Their logs only detected a cylinder 1 misfire every 5-10 miles and that was about it.
The bucking is inconsistent as well, some bumps dont make the car buck, and some right turns dont do it either. I have noticed the car bucks on right turns the worse when at lower rpms, but it still doesn't do it every single time. I have no CELS and i dont know what to do at this point.
I've been told it can be 100 different things, and because i have no codes i really dont know where to even begin. i dont make a fortune to just throw money and parts at it either.

I dont have an Accessport and the car is stock from what i know other than a Cobb BPV, K&N Short Ram Intake, and a resonator delete. It has 145k miles on it

Also to mention i've tried cleaning my MAF sensor (didnt change anything)
Tried putting in the old spark plugs (took out my NGKs 6510)
Pulled fuses ( everything seemed okay)
and bypassed my fuel pump resistor

In a real pickle and i cant seem to find ANY kind of answer from anyone.....hoping i can get some ideas here. Im a new member here and ive seen alot of others find answers here...just testing my luck! If not, i might have to cut my losses and roll over the rest of what i owe to get something else
I love my Ms3 and i just wanna get her fixed.
ANY and all help is appreciated!
Im new to the car enthusiast world so give me break okay hahaha

Also ive Only have had the car for 6 months and im pretty sure i need my VVT to be checked cause there is a bad rattling noise on startup

 

Welcome to MSO!
With those mods you shouldn't be running colder plugs, run stock heat range NGK 6509, ensure your plugs are gapped to 0.026-.028" since it started when you swapped plugs perhaps you need to restretch the springs in the coil packs, give that a try.

Did you touch anything else when doingp lugs?

There's also a ground near the hpfp make sure that contact is clean and tight, also check the grounds to the chassis near the battery do the same.

145k and rattling noise on startup vvt is certainly past due.