According to MINI USA the sat nav is $435 and the click and drive system is $150 = £$585. I bought mine in UK for £265 all in.Does the Garmin app say it's compatible with Mini Connected?
Mini Connected doesn't seem to work with any other apps then it specifies, and Garmin is not one of them at my last check (I think).
You do have the option in the US of buying the Mini Portable Navigation which attaches near your speedo cluster for not a vast amount of cash. It's oddly expensive in the UK.
Your other option is to get a CravenSpeed iPhone Mount, as they are super neat mounts for Minis.
The click and drive will accept any Garmin unit.