Is the sentence omnis res est ("every thing is") grammatical? Likewise, are sentences like aliqua res est and nulla res est grammatical?
While everything in your answer is correctly inflected, I'd argue that it's actually not a correct construction.
Firstly, the use of 'res' for 'thing' is not a very common construction; 'res' is nearly always better translated as 'affair, issue, matter' among others, but usually not 'thing' in a general manner as you mean. Latin generally uses a neuter gender adjective. So in your case you should be saying 'omnia sunt' (plural, not singular as I'll explain), 'aliquod est' and 'nihil est' ('nullum est' is rare but you could probably get away with it).
Secondly, the word 'omnis' should really be plural. 'Omnis' is better translated as 'all'; it is a quirk of the word 'everything' in English that we always use the singular verb instead of the plural, but this is not the case for 'omnis'; we use the plural for countable nouns in the plural. For uncountable nouns or singular countable noun, 'the whole' or 'the entire' is a nice translation for 'omnis'. So 'omnis res' actually translates to 'the whole thing/affair/matter/...', which is quite different to what you're trying to say. The use of 'omnis' in the singular to refer to the plural I have seen before, but only ever in poetry, where the poet might do this in order to obey the rules of scansion. So I wouldn't recommend it.
Each of those sentences, meaning "every thing is," "some thing is," and "no thing is" respectively, is complete grammatical sentence when one uses esse ("to be") in the sense of the "thing" exists (existential), rather than the thing is something else (complementary).
However, it seems like a rather odd sentence in my opinion. In English, we don't separate "every" and "thing," but combine them into one word: "everything." Latin, likewise, has a similar single word that contains the same meaning, and would probably be used more often/sound more natural.
- Omnia sunt
- Everything is
- Aliquid est
- Something is
- Nihil est
- Nothing is
Now, if you are insistent on using them as separate words, it could emphasize the singularity (a one by one sense) of each item in the whole. But this is only a feeling I get from English, so I do not know if it transfers to Latin, so that is why I suggest the options above. Esse can serve in an existential sense, as I already mentioned. Res can often be omitted and is replaced instead with a neuter adjective/pronoun, which is essentially what options 1 and 2 are.
Also note, this is merely a grammatical analysis, and doesn't particularly examine any historical examples. I did search a bit on Perseus, and found no examples, but there may still be some out there I did not find.