I suppose turning on the RPi is easy - make sure the RPi power is connected to a power connection in your car that turns on when the car door is unlocked, door opened, or car started.
Turning off with a delay may not be needed, depending on the OS you use for your RPi.
I could be wrong, but I think embedded Linux is OK with instant power off, and should be available for RPi.
Example: LibreElec runs on an embedded Linux version - granted, LibreElec is intended for a media player [KODI], but it shows that such a distro should does exist - there are a few articles out there that should get you started, like this article.
* This to prevent filesystem corruption when the RPi is powered off.
You could of course add a small battery, for example a cheap power bank, to buffer the power when power is lost - this would make things a little more complicated as one needs to detect power loss and power being turned on again.
So from a on/off/hardware perspective this should work.
Now, modifying the boot image can be done like so (source - I have not tested this):
- In your favorite image editor create a splash screen and save it as splash.png.
Choose a 1920 x 1080 resolution as it scales well with 16:9 resolutions.
- Copy the image to a USB flash drive and insert the drive into the Raspberry Pi.
- Copy splash.png from the USB flash drive to your home directory /home/pi/
- Open a Terminal on your Piu and change directory to the location of the original splash screen for your Pi.
$ cd /usr/share/plymouth/themes/pix/
- Optional: Backup the original splash.png file to a file called splash.png.bk
$ sudo mv splash.png splash.png.bak
- Copy your splash.png to the current directory. This will copy the freshly created splash image ready for use.
$ sudo cp /home/pi/splash.png ./
- Reboot your Raspberry Pi.
Once your Raspberry Pi reboots you will see the familiar rainbow screen, and then a few seconds later you will see your custom splash screen.
Disable boot rainbow
The rainbow at boot can be disabled by adding this to the config.txt file:
This should not affect the splash image.
For this you can either use an ODB2 device (cheap and probably easiest) or a GPS module. The ODB2 module provides much more car related data, like RPM etc. Here is a project I found at Instructables that hooks up a ODB2 dongle to your RPi (GitHub backup of that same article).
Hope this helps to get started.