No, it is not a proxy for another search index/engine.

Yes, you can add Brave search to your other browsers.

I wouldn’t stress much. It would take a targeted attack to have actually compromised your phone. It is alright.

It removes more proprietary binary blobs and I dont care about gapps.

I heard that he was a scammer or pseudo privacy expert from other comments. I wouldn’t recommend that phone. If you care about the privacy or security of your device, use DivestOS with a supported Pixel/OnePlus, or GrapheneOS with a Pixel. Only buy the phone new if you are super paranoid of some zero-day vulnerability being used on you. I recommend swappa.com because they have quality control, returns, and good prices for used devices (you can even get mint quality devices).

Comparison of Android ROMs: https://eylenburg.github.io/android_comparison.htm

iodeOS has been behind on security updates often (still better security against unsophisticated attacks than Ubuntu but not a good ROM): https://divestos.org/pages/patch_history

My recommendation is GOS if you care about out of box experience and using gapps, DivestOS if you care about degoogling and removal of proprietary code. Both are hardened.