@errant @sidereal @nullagent (1) Baseband: No, but it's not supposed to have any control over the computer the radio is attached to. Does it? That's a good question that's under-researched.
(2) Can you stop updates? Yes, absolutely.
(3) Play Services? If it's a good alt OS, no, there's no Play Services (LineageOS, etc.), or Play Services is sandboxed and defanged (GrapheneOS), or no Android at all (PostmarketOS).
(4) Pull location from baseband? If you're connected to the cellular network then yes that's announcing your location relative to towers. When not connected to that, no, they can't. And that only links the IMSI (SIM card number & identity it was purchased under) to the location; it doesn't link software on the mobile computer *unless* the software is backdoored to cooperate.