Should I start putting my phone in checked baggage? Is that allowed with the batteries and stuff? I guess I can carry a cheap older smartphone with a burner number for the actual flight.
Before entering authoritarian countries, you should factory reset the phone, add a minimum contact list, and have a process for restoring what you need from the cloud. No need to store phone in luggage.
Also better to leave the laptop at home, if you don't want to wipe it.
Not in any airport I have been to. Usually it's landing -> immigration (border control) -> baggage claim -> customs (just walk through if you have nothing to declare) -> exit.