Is the word childs ever used instead of children for the plural of child? And was it ever a part of standard English vocabulary but later neglected?
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 :)
Etymonline has this to say:
in the names of sciences or disciplines (acoustics, aerobics, economics, etc.) it represents a 16c. revival of the classical custom of using the neuter plural of adjectives with -ikos (see -ic) to mean "matters relevant to" and also as the titles of treatises about them. Subject matters that acquired their names in English before c.1500, however, tend to remain in singular (e.g. arithmetic, logic).
So yes, at some point in history, there were such things as physic (meaning "natural science"), mathematic (meaning "mathematical science"), etc. that were later turned into plural forms but kept being treated as singular.
Edit: having looked in a few more places, it appears that in contemporary English, it still makes some sense to have both the suffix -ic and its plural form -ics. According to the Collins English Dictionary, the former has kind of specialized in forming adjectives, while the latter is happily forming nouns:
suffix forming adjectives
- of, relating to, or resembling: allergic, Germanic, periodic. See also -ical.
[from Latin -icus or Greek -ikos; -ic also occurs in nouns that represent a substantive use of adjectives (magic) and in nouns borrowed directly from Latin or Greek (critic, music)]
suffix forming nouns (functioning as singular)
- indicating a science, art, or matters relating to a particular subject: aeronautics, politics
- indicating certain activities or practices: acrobatics
[plural of -ic, representing Latin -ica, from Greek -ika, as in mathēmatika mathematics]
The key here is that they are not just two unrelated suffixes. Much rather, one is etymologically a plural form of the other. As the American Heritage Dictionary succinctly puts it, -ics is "-ic + -s".