Harry A

Hello people, Quite recently bought my first 350z. It is an import but has lived most of its life in the UK. Recently having some problems. Rough cold start, rough idle and acceleration juddering. Here some notes I have bullet pointed in case this helps anyone. Judder always happens between 2000 - 2250 RPM Cold start sounds rough, idle sounds rough. Car has been mapped before (believe to be back around 2019 by a previous owner) Problem has occurred since last battery started dying. (Could just be me overthinking) Seems like it has started doing this every time is wet weather (could just be me overthinking) Immobiliser has recently been playing up, not sure if this could play a part in it. I have got videos but won’t let me post.