On the proportion of Nucleotides in the Genome and what it can tell us about Evolutio

Well, that depends on exactly what's going on. If we have a scenario as in "case 2" in my previous post, then no. In that case the AT content will have an equal chance of taking on any value. Note that this does agree with your intuition that "every nucleotide position, after several mutations, [will] have a 50% chance of being AT or GC" --- but only because 50% is the average of the numbers between 0% and 100%. 50% would therefore be the "expected value" only in the statistical sense of being the mean average outcome, not in the sense that we should particularly expect that the AT content should have that value rather than any other.

Well, that depends again on what exactly is going on. What you're modeling there is where the mechanism for mutation is "Pick a base at random, then change it with equal probability to any base it isn't". This is somewhat simplistic.I have done a model of that case, and you are right: the probability distribution does indeed spike around 50% AT. I also find that biases in the probability of mutations and their repair shift this spike with relative ease: if, for example, a change from AT -> CG is twice as likely to be repaired as one from CG -> AT, then this shifts the spike to more like 75%.

It seems that it would be more accurate to say that it's of the order root n (using "big O" notation).Here's a graph of values for n between 1 and 10000: The blue line is the square root of n, the red line is the average of |h(n) - t(n)| over ten thousand trials.

The only answer anyone can give you would be: similar to that of a closely related species. For example, the figure for humans should be close to that for chimpanzees. But there is seemingly no a priori method by which one can readily predict the AT content of a species.