You can write a program that solves the halting problem SOME of the time, but not ALL of the time. So, there will always be some inputs for which your program will either not halt or give a wrong answer.

That's a good point. However, it's not so simple to rule out programs referring to themselves. They might refer to themselves indirectly via another program or not to themselves at all, but to a near-copy. There are also ways of defining incomputable problems where the reference is not internal to the programs themselves but indirectly through the problem definition, such as the Busy Beaver problem.

In a computer, W is represented by a sequence of 8 bits, specifically, 01010111. It is common to represent a 1 using 5 volts and a 0 using 0 volts. I don't image these facts really help, but they answer your specific questions, anyway. In my intro course, I try to explain things in a lot more detail.

You're right, there is a timing dependency. (Of course, real circuits have such dependencies as well!)

I have a copy on my desk and the cover is very clever. I haven't had a chance to read it yet. Thanks for the recommendation!