First of all, I'm currently at work and not in the opportunity to thoroughly respond with quotations and references.

In response to your questions:

1) The use of 'Ockham's Razor' to prove or disprove the existence of God.

It must first be clear that this so called razor was not solely property of Ockham, there were thinkers before him who used the same principle, and it was later that Ockham was recognized as a profound practisioner of this scientific principle.

Secondly Ockham did not use this principle to prove or disprove God. He used this principle to show that God cannot be proven or disproven, that reason or rationality (philosophy) can only conclude to philosopical c.q. conceptual gods.

2) Why is Ockham's razor appealing?

You make it look like that this principle to not allow unnecessary entities in your ontology (explaining the world by for example an appeal to flogiston or aether, or god for that matter), is appealing due to some non-rational dispostion. Because simplicity is aesthetically or sentimentally appealing.

This principle of only deciding for theories that only have neccessary elements in there hypothesis or axioms is not appealing just because, but for it's inherent logical validity.

If hypothesis x sufficiently and neccessary shows that p, than an alternative hypothesis x + flogiston would be a thought to many.

This way of thinking is exemplified in Ockham's work in which he shows his conceptualist/nominalist epistemology.

Let me give it a go.

"It is vain to do with more what can be done with less."

Occam's Razor: Or The Law of Parsimony

The law is stated thusly:

'Entities should not be multiplied needlessly.' What this rule means is that, out of two or more competing explanations that explain the exact same data, the one which is simplest is the most epistemically sound. Another way to look at the razor is as a dictum that any explanation for unknown phenomena should first be attempted in terms of what is already known.

The key points are

1) Ockham's razor does NOT say that whichever explanation is simpler, is 'true'. It states that if two theories equally answer a question, the simpler one is more epistemologically sound, because the second one appears to include unnecessary elements.

2) A theory that relies on what has already been substantiated through evidence is superior to another that relies on unproven claims - in other words, any "answer' that creates more problems than it solves is hardly an "answer' in the first place.

A more thorough examination of Occam's razor, by Philosophos, from infideguy.com

Which is more parsimonious: the idea that our planet and its inhabitants got to be the way they are by the long, slow work of natural processes that we have largely already identified or that a race of super-advanced alien beings built the whole works with the appearance of great age as part of a massive philosophical experiment? The natural explanation is more parsimonious and so it would be favoured by Occam's Razor. So, if it turns out that the planet really was created by Slartibartfast and his crew, that would be a failure of Occam's Razor.

My thinking is that a less-fanciful, real-life example of such a failure -- or a claim of such a failure -- might be useful in discussing the question of whether or not Occam's Razor is justified.

Okay, let's look at this in more detail and more abstractly for a moment.

There are two competing theories, H0 and H1, and we'll take both to adequately explain a given body of information I. How are we to choose between the two? Occam's Razor states that we should choose the more parsimonious one, which we'll let H0 be.

Now, suppose new relevant data D comes in. If H0 and H1 both explain I + D, we're still left with the same problem. But if H0 doesn't explain D, and thus I + D, does Occam's Razor tell us we should still accept H0? No, since it no longer explains the data, even though it's simpler.

In terms of your example, you have a key phrase: "So, if it turns out that the planet really was created by Slartibartfast and his crew, that would be a failure of Occam's Razor." How could it "turn out" that we'd know that the planet was created by Slartibartfast (H1)? The only way I see it is that new data, D, came in that the Slartibartfast theory is consistent with, but the natural law theory isn't. Thus, Occam's Razor no longer applies, since the two theories no longer are consistent with the known data (it used to be I, but now it's I + D).

So, again, I'm not sure how Occam's razor would fail. If new information comes in that one theory isn't consistent with, then the conditions for using Occam's Razor fail (it requires two or more theories that adequately explain the known data), not the Razor itself.

If you're not buying my explanation, and still want an example where Occam's Razor "failed" in the way you described above, then the precession of Mercury's perihelion is a good example. There were two explanations for this: either Einstein's relativity or Newtonian physics plus a correction factor (for example, a large dust cloud between Mercury and the sun). Which is simpler: the well-established theory plus the postulated existence of one thing (the dust cloud, although there were other proposed corrections) or a new physical metatheory which is much more complicated mathematically and based on less (really, no) physical law? I'd say it's Newton's theory plus the corrective factor: it doesn't require a replacement of a seemingly adequate theory with something quite new.

If you agree with this, then let's continue. People started looking for said dust cloud, and found none. The other corrective theories also turned up naught. And so, General Relativity, the more complicated theory, was slowly accepted into the mainstream as new data came in negating the ad hoc corrections to Newtonian physics. So, in the sense you stated above, Occam's Razor "failed" (in your sense of the word, which I argued against above).

As an additional side note, it was argued in the paper Hookflash linked to earlier that Relativity was actually the more parsimonious theory, and for good reason. I think that the idea of parsimony isn't precise enough, and that it can be reasonably be broken down into two subtypes: what I'll call front-end and back-end parsimony. Front-end parsimony is the type you described above: the theory looks more complicated to work with up front. Back-end parsimony is something that I feel is less subjective: it's the sharpness of the predictions made by the two theories. For instance, the Slartibartfast theory lacks back-end parsimony because it makes many more predictions than the natural law theory does. Natural law hedges it's bets. For instance, the Slartibartfast theory gives no good reason for the ubiquity of the genetic code, for instance. Why not have varying genetic codes among the different species? It could happen under the Slartibartfast theory. Natural law does through common descent. Thus, back-end parsimony talks not of how complicated the theory looks, but instead how much is possible under the theory. Relativity was back-end parsimonious compared to the corrected Newtonian theory because the latter had an additional freely floating variable that had to be fixed only upon incorporating the Mercury data into account. It was capable of predicting more by sliding the variable's value around (for instance, how big the dust cloud was). Relativity had no such variable, and thus, although it had less front-end parsimony in my view, it had greater back-end parsimony.

These concepts correspond directly to the Bayesian concepts in Hook's paper of the Bayes Factor and the Odds Ratio. The former can calculate (free of prior probability assessments) how much the theory does or doesn't rule out, and the later is how complicated the theory looks, which makes people more dubious of using it (although it's subjective). The Bayes factor measures what I've been calling "back-end parsimony" and the Odds Ratio measures "front-end parsimony" (which is subjective to an extent).

See also: http://parallel.hpc.unsw.edu.au/rks/docs/occam/