Thank you for your answers.
I've done tests without the MOSFET and it draws less than 10mA, I tried the LowPower library but it broke my timing code (it dropped the current needs to 4mA) so it was a no-go so far. Compared to the humongous power reserve in my Car battery it really isn't a concern. The ADXL is very low power to start with, but there's room for improvement. I also read about Rocket Scream low power pro minis
and it may help to squeeze a few more mA. I also tried to put the arduino to sleep and only wake it up using the ADXL362 interrup, but didn't really found the sweet spot I was looking for. I first want to have a proof of concept before trying to optimize it, but I already searched that topic.
I want to power to output while moving, especially during long rides ever straight soft ones. I did many test drives and tuned my code accordingly. I have a satisfactory sketch right now (it works as intended, even if a bit hackish), but there's room for improvement (that's partially why I left the processing on the arduino instead of offloading this par to the accelerometer)
I thought the LM7805+Caps were enough to provide a safe power source to the Arduino, I really lack knowledge in the power department, I'll try to document myself on this topic, but there's a lot I don't know.
The on-board regulator of the pro mini is rated 12V tops, and a car battery can exceed this easily. using a LM7805 permits to lower the voltage to a much bearable 5V first. I prefer to heat the LM7805 than the arduino board
The wires already run into my car where I want them, so I didn't even try to me a wire.
Again, thank you for your answers and questions, it points me in a few directions I didn't thought about.