Learn English – the proper plural of the word “freshman”

This lack of respect for the language of origin not a phenomenon unique to English. When a word is borrowed into one language from another, unexpected things can happen.

I would argue that, for many examples you've given in your question, the actual perception of a singular-plural relationship is messy in practice, and the application of the plural is inconsistent.

Data: Using data as a collective noun with singular agreement is more common than using it with plural agreement. More in another thread from this site.

Alumni: I have heard as many people also use alumni for the singular, or even alum, as I have heard use alumnus for the singular. I imagine my experience with this word is typical (at least in the US), though certainly not universal. In any case, it is messy.

Media: The words media and medium don't even seem to correspond in any meaningful way in actual English usage. The word media has forked off and become a different word entirely. The word media is clearly used as a collective singular noun, as shown in newer constructions like multimedia (not multimedium even though we don't say multistages, multicores, multicycles, multistories, etc.). You will find few people who will ever say "Mass Medium". We talk about someone having "media savvy" even though we wouldn't say "computers savvy" (even though they can work with more than one computer). This is because, in English, these sorts of constructions always use the singular noun, whether it is collective or not. The way that media is used is evidence of how the word is actually parsed, perceived, and used by English speakers.

Another example of how foreign language morphology often doesn't mesh well: people try to pluralize octopus and virus as octopi and viri/virii, respectively. Virus was a mass noun in Latin, where we got the word. The word octopus comes from Greek and would take the plural form octopodes in Greek.

My main point is this: there is only a weak, inconsistent application of this -us to -a or -us to -i to begin with. So forums (like statuses and others) is a word even though we also sometimes have this other rule. Our language seems to continually push us towards either dropping the foreign pluralization in some way or another, or reanalyzing the plural as another distinct word. So I see this confusion as the language trying to mash these words around to make them fit our language naturally.

If we hadn't become so darn literate and knowledgeable in the past few centuries, I imagine these plurals would have regularized by now :)

Cost is typically left without the s if there is only one purchase:

The cost of thread

Using costs here would imply more than one type of cost:

The costs of homeschooling

You can still say this without the s but the connotation shifts back to one solitary cost:

The cost of homeschooling

It is ambiguous whether these costs are monetary or emotional or something else. Referring to bundles of purchases will typically use costs:

Needle costs are rising

These are my needle costs

If you used cost here it would shift back into a description of needle markets or a single project's purchase:

Needle cost is rising

This my needle cost

The differences between cost and costs in these examples are subtle and could be entirely regional. One final note is referring to how much something costs. This will follow standard pluralization rules:

The book costs $4

The books cost $4

To directly answer your question, I would use costs: Sewing Material Costs. Variations:

Sewing Material Costs — the money spent on sewing material over multiple purchases

Sewing Materials Cost — the amount required to buy "sewing materials"

Sewing Materials Costs — the amount spend on sewing materials over multiple purchases

Savings is most typically plural in the sense that you are using it:

Our savings on needles are significant

These are my coupon savings

I have $300 in savings

What you want to do is replace "coupon" in the second example with "Material Costs":

Material Costs Savings — the savings on "material costs"

The use of "costs savings" is probably what makes this seem strange. The idea that you are accumulating savings through costs is counter-intuitive. But you aren't saving through costs, you are saving on costs. The alternatives are not quite what you are looking for:

Material Cost Savings — the savings on the price of "material"

Materials Cost Savings — the savings on the price of "materials"

These don't make much sense to me. I don't think "savings" works well with "cost".

Materials Costs Savings — the savings on "materials costs"

This works but the extra plural is even more distracting. This form would work better with other objects, however:

Needle Costs Savings

Car Costs Savings

You can to try to use a hyphen to reduce the awkwardness:

Material-Costs Savings

But I would just stick with Material Costs Savings.