It might be useful to consider why checkerboards are good shape in legal systems, but bad shape in go. Also why the legal system rejected checkerboards after some thought, at least provisionally.
(historical rant: You might as well resign if your opponent is not also 30k. Who comes up with these analogies? People who have barely heard of the game, like 10ks or sth?)
Finally: yeah, Go is a bad analogy for this.
The analogy breaks down because 'being allive' would require access to the edge, rather than having two liberties. Playing with such a different definition of life and death does seem like an interesting 'variation' of go.
You have mashed some words together and they do not make sense if you know what you are talking about.
A diagonal connection is a very thick connection. The major complaint about this connection is that it is not efficient; hearing someone say that the stones are not really connected is, once again, just hearing that you are 30-20k. I am being generous about 20k.