Question

1. Compare your physical computer (or any given physical computer really), to a Turing machine. Are they logically identical? If not, what is the main difference?

Answer 1

A Turing machine is an abstract, notional machine which can compute more than any physical computer. This is because your physical computer has access to only a bounded amount of memory & your computer's processing speed is limited by various real world constraints. Another comparision is that, a turing machine typically don't need an I/O device i.e, the input is provided on input tape, and when the machine is turned on, the output is recorded on the tape, and the machine halts. But your physical computers always needs an I/O device to interact with the user.

Yes, they are logically identical. A turing machine input tape is closely equivalent to the combining efforts of computer's memory plus I/O devices(as it can provide some extent of  unlimited "tapes", but not an infinite amount of it).So we can say that a physical computer can simulate a turing machine.