Anything that's turning complete, has enough ram, and has a c compiler can run Linux. Theoretically, you could program a CPLD to run brainfuck and you could still run Linux.
Yes. Any turing complete processor can perfectly emulate any other turing complete processor, whether it is x86, arm, or riscv. Mainline Linux can then run on this emulated processor without modification.
I respectfully disagree. The turning machine is not doing any set-up before the emulated CPU begins execution, and all of the actual BIOS is done by the emulated CPU.
I'm not sure I understand your argument. Are you saying that the emulated processor executes instructions while the SoC doesn't? Every instruction that goes to the x86 is broken down into several SoC instructions, which the SoC executes in order to emulate what an x86 would do. Saying that the emulated x86 is booting/running Linux, but the SoC is not is like saying that computers can't run java code, they can only run jvm.
I'm saying it runs it because "running" is transitive, but doesn't boot it because "booting" is not. Similarly to how you can carry your grandkid by carrying your kid who carries their kid (carrying is transitive), but you can't give birth to your grandkid by giving birth to your kid who'd give birth to their kid (giving birth is not transitive).