Rpi 4b as car audio player over bluetooth?

Hi,

I'm expanding my multiroom setup, have three players (2x Rpi 4b and 1x Rpi Zero W) with Hifiberry DACs and Amp2 stationary in my house.

I have another Rpi 4b with Hifiberry DAC that I would like to use in my car as input to the car amplifier via RCA cables. For this it would need to function over bluetooth obviously without wifi present. When the car sits in the garage with full wifi strength it would be awesome if it can sync with the rest of the multiroom system. For this obviously the car needs to have the key in, which is no problem as it's got an off-grid battery pack. I bought a 5v/a3mp step down power supply to feed the Rpi.

There's 2 problems;
1. I can connect my iphone over bluetooth with the Rpi, it shows connected, but it's not listed as output option in Ios for Spotify/Soundcloud or as output from the navigation app. Are there any specifics that I need to do in terms of settings?
2. It would be nice if the Rpi with PcP could boot up bluetooth quickly so eveything works when driving off, anything to tweak there? Also, are there any issues with just powering down the Rpi by just killing power? Would it possibly corrupt something?

Many thanks in advance for help.

Gr. Nelis