from your link:

It is used to criticize a totalizing view of science as if it were capable of describing all reality and knowledge, or as if it were the only true way to acquire knowledge about reality and the nature of things;

That's a pretty good summary of what I mean by the term.
John Lennox, Professor of Mathematics and Fellow in the Philosophy of Science at Oxford, writes of it like this:

Peter Atkins gives a classic expression of this view: 'There is no reason to suppose that science cannot deal with every aspect of existence.' That, in a nutshell, is the essence of scientism

Further, he writes:

Scientism does not need to be refuted by external argument: it self-destructs… For, the statement that only science can lead to truth is not itself deduced from science. It is not a scientific statement but rather a statement about science, that is, it is a metascientific statement. Therefore, if scientism's basic principle is true, the statement expressing scientism must be false.

Yes, I would mean empirically demonstrable. As I stated earlier, if something cannot be detected, then in what sense could we say it exists. This is the purpose of faith – belief without evidence, or in some cases to spite the evidence.

Again, by 'detect' you seem to mean 'detect scientifically'.
I also dispute the definition of faith as belief without evidence – that is not necessarily so, and in the Christian context I don't think you would find too many serious thinkers from any century defining it as such. Indeed, the NT writers tend to emphasise reasons why their readers should have faith (i.e. 'put their trust in')

Of course, this approach does not deny that things outside our experience absolutely do not exist, just that we cannot say either way. The issue is unanswerable and irrelevant (since such things have no effect).

While I would agree that God, as a supernatural agent is not scientifically detectable (as science's scope is the natural) that doesn't mean we can have no experience of him, as I'm sure most Christians would agree – the only way you can sustain your claim of lack of experience is if you assume a Scientistic ideology that denies the validity of other disciplines and experiences. While it is right that empirically we can not say either way, that doesn't mean there is no reason to have a position either way – indeed, we both seem to have made a position, albeit is opposite directions, despite this lack of empirical demonstration.

The inclusion of purpose in premature. First you should demonstrate there is a purpose before we can discuss what it might be.

No, the inclusion of the concept of purpose demonstrates the insufficiency of the Scientistic ideology. Purpose is one concept that no amount of scientific analysis can necessarily answer. That is not to say that in every case there must be a purpose, I simply refer to the concept, and as long as we can agree that for some things there is a purpose, then it is a concept that science cannot give the answer to.

The purpose of a cake is determined by ourselves – mostly they are for eating.

Actually, no amount of scientific examination of the physics and chemistry of a cake will tell you that it isfor eating, though it would no doubt tell us that it is possible to safely consume. To determine the purpose, broadly that it is for eating, requires other knowledge than physics and chemistry. More specifically, while it may be able to say that the icing is blue because of certain chemicals or pigments, it won't be able to say why it has blue icing instead of pink – and such investigation will certainly not be able to tell us who (if anyone) the cake was made for. That requires revelation – it requires Aunt Mildred herself to tell us that she made it for her nephew. What this analogy demonstrates is that there are questions which science is unable to answer – that is no insult to science, indeed, the opposite is so, claims the Nobel Prize (1960 – Physiology & Medicine) winner Sir Peter Medawar. He writes:

There is no quicker way for a scientist to bring discredit upon himself and upon his profession than roundly to declare – particularly when no declaration of any kind is called for – that science knows, or soon will know, the answers to all questions worth asking, and that questions that do not admit a scientific answer are in some way non-questions of "pseudo-questions" that only simpletons ask and only the gullible profess to be able to answer… The existence of a limit to science is, however, made clear by its inability to answer childlike elementary questions such as: "How did everything begin?";"What are we all here for?"; "What is the point of living?".

The "purpose" of the bacterial flagellum is to provide propulsion, but the "purpose" is a descriptive term of what it does, not evidence of intention.

I agree – that's my point – no amount of scientific study of the thing itself can tell us anything beyond what it is and / or does – it can say nothing what it is 'for'.

Let me ask you this: what possible purpose does an omnipotent being require the creation of a universe to achieve? If the answer is unknown or unknowable, then how could you say there is a purpose at all?

You might just as well ask 'what possible purpose does an old Aunt require the baking of a cake to achieve?'. The answer is as I pointed out 'scientifically' unknowable, but that doesn't mean there is no purpose at all – it just means we have to rely on her revelation of that purpose. There may very well be no purpose to her cake, but the answer must come from her, and cannot come from scientific investigation of the cake itself.

Science observes reality.

That is true. But it is quite begging the question to suggest that either science is the only means to knowledge, or that only what science can observe constitutes reality. Indeed, those positions are self-refuting as they are not scientific statements themselves.

If you have evidence, then what do you need faith for?

If I put faith (i.e. trust) in a person, it is because of evidence and reason that I think they are trustworthy.

Nuff said.

And if anyone cared to actually read Hebrews 11 they would see that the writer goes to greath lengths to show how God has been faithful in the past and why they should have faith (i.e. trust) – notice how he concludes at the start of chapter 12:

Therefore, since we are surrounded by so great a cloud of witnesses….

so you see the writer is in no way suggesting anything like your interpretation claims, quite the contrary.

If a supernatural entity has an effect, we should be able to measure it. If we cannot, then how could you say it exists at all?

Again, just an assertion of your Scientism: only science is the way to knowledge.

Show me another “ideology” that works and I will be interested.

One that allows for other disciplines like philosophy and literature would be a good start…

I have not made a decision, I do not believe due to the lack of empirical evidence.

So you do not believe that the universe is causally closed?

Don’t confuse this with design either. While we might design a car to transport people, there is no way we can determine if the crab’s shell was designed in the same manner. That’s the problem with inductive reasoning.

I don't believe I've said anything about "biological design", have I? In any case, it remains that no amount of physical and chemical investigation of a car will tell you it's purpose either, it will tell you that is moves, that it has a combustion engine and so forth – but you need to go beyond physics and chemistry to see that it is for driving people.

Your right – it won’t. We assign purpose to objects, it’s not granted to them by mystical beings.

So you acknowledge that in the context of a cake, an external causal agent who created it with a purpose is acceptable, but not in the case of the universe itself?

It sure does – the fact we have observed people cooking and eating them in the past. The fat we ourselves have seen and eaten cakes in the past and enjoyed them. Evidence.

Yes, it is evidence, but that is not empirical science, it is a different kind of evidence, sociological, but physics and chemistry it 'aint – and it brings in the big philosophical problem of induction. Indeed, this cake may be for throwing at local politicians in order to raise money!

Or you could ask the cook.

Yes, indeed – which is why I said "That requires revelation…”

That IS science.

No, it's not – it's personal revelation – you can't test it, you can simply either accept or reject her testimony.

That does not grant you license to invent answers.

I think there'd be plenty of philosophers who would object to your assertion that what they do is simply invent answers! (as indeed, Medawar concludes that it is to philosophy and theology that we must turn for answers to questions such as those)

Are you setting up an equivocation error to claim spiritual “revelations” are the same as actually asking someone why they cooked a cake?

how is it equivocation to compare one external agent revealing their purpose to another external agent revealing their purpose? (equivocation would be to say something like: He's a bright boy, so I better put on my sunglasses)