2024 Limited purchased new less than a week ago -- vibration, weird noise in back, sputtering with acceleration?

I want to know more about the issues mentioned in the topic. None of these things were noticed during the test drive last weekend but started showing up a day or two ago; they were all noticeably worse this morning.
I had been attributing the vibration to something simple, like a tire issue or whatever. Then the sputtering when accelerating in the lower RPMs thing started. We will more than likely tell the dealership to take it back (they told my wife we have 7 days to do this, but I'm sure there's a bunch of usual dealer bullshit caveats she didn't ask about that'll make it a PIA) and look at the other options we considered. However, I always want to know as much as I can to be prepared for interactions like I'm about to have and appreciate whatever may be contributed.
Also, I know there's a search function and I am making use of it as well to gather all the info I can.

Thanks in advance.

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