Is -1 followed by a singular or plural noun?

A few elements of response:

1. authority: as mentioned by Cawas, there is not ultimate authority on the English language, and while there are a number of references, I have not been able to identify a solid consensus on the subject.

2. Usage: It is fairly difficult to check this due to the possible misunderstanding between "(minus one) thing" and "minus (one thing)", assuming that these are two separate cases, an assumption I would tend to disagree with. However, searching for "minus one dollar" -infinity on Google returns 254,000 results while "minus one dollars" -infinity returns only 7 results. The difference is significant enough to consider that regardless of any possible confusion as suggested above, minus one should be followed by the singular, at least in this case. ("-infinity" is added to the search phrase to exclude the expression "infinity minus one dollar"). "minus three dollars" is significantly more common than "minus three dollar", suggesting that "minus" itself does not affect the rules of the plural/singular following numbers.

3. Logic: "minus one" is not an actual quantity in the physical universe. "Minus one" is only an abstraction which refers to the action of subtracting one of anything. Rather that saying "whenever you have apples, remove one apple" we say "minus one apple". It follows that "(minus one) thing" and "minus (one thing)" are actually equivalent.

Barring incontrovertible evidence to the contrary, I would say that it is safe to use the singular following "minus one".

As I said in answer to another question (about "0.25 mile" v/s "0.25 miles"), my preference is to use the singular only for the natural number 1: when you are counting something and the count is 1.

That is, if "minus" is conceivably an operator, as in "the band reunited, minus one member", you would use the singular. (The "one" there is a count of how many members were missing, so it takes the singular.)
But if "-1" is just a numerical value, then (to me) the plural is preferable, as in "It was a cold day in winter, and the temperature was -1 degrees Celsius". This is similar to the usage "0.1 grams", IMHO. (Though what I'd actually write is "-1 °C", side-stepping the issue.)

(Searching Google for "minus one degrees" gives this article and this one, but make of them what you will.)

Neil Whitfield gives an answer on his ESL blog here. It depends on whether the quantity is countable or not.

[C]ountable nouns form plurals; mass/uncountable nouns don’t. This gets a little more complicated because some nouns may be either countable or mass/uncountable, depending on how they are being used. “Wheat” for example may be both: ten kilos of wheat is uncountable; several types of wheat is also uncountable; there are several wheats used in this mix is countable.

OK, with countable nouns: I would say 0.1 apples for grammatical reasons, though I agree it is not logical! I guess you could say 0.1 of an apple just as you say one-tenth of an apple If the number one is used, whether it is +/-1, the following noun will be singular. So it would be -1 apple. We’re talking grammar, not logic; and yes we say zero apples, probably because zero is thought of as a number that is not one, even though zero is neither singular nor plural logically.

So it looks like grammatically (perhaps not mathematically) the following

• 0.3 = point-three apples (uncountable)
• 1/3 = one third of an apple (countable one in fraction)
• 2/3 = two thirds of an apple (countable more than one third)
• 0 = zero apples, no apples (uncountable)
• 1 = one apple (countable)
• 3 = three apples (countable)

However (caveat, I'm not a grammar professional),

• -1 = negative one apples (uncountable, you can't have negative of something real, like money. This is a mathematical concept only, hence plural would be OK.) This feels like negative-one apples
• -1 = minus one apple (countable. "After they broke into his house, he was left with minus one apple." The number of apples stolen is countable.) This feels like minus one-apple

I hope that clarifies it a bit more. They're both appropriate in different circumstances. Hooray for English! #sarcasm

I'll add just a bit more. If the word one can be replaced by an article (a/an/the) then you should use the singular.

• The temperature is minus one degree Celsius.
• The temperature is minus a degree Celsius.

However, the following is kind of awkward:

• Ten subtracted from nine is negative one degrees Celsius.
• Ten subtracted from nine is negative a degree Celsius.

So you should probably use the plural.

The only number that is singular is one. All other numbers are plural, including negative one. 1.0001 is plural. 0.99999 is plural. 0 is plural. -1 is plural. Only 1 is singular. The nature of singularity is being single, unitary, unique, isn't it? Everything else is plural.

However, in many cases the string of words "minus one" does not denote a negative number. Rather it denotes a relation with the preposition minus and a singular item. In the questioner's examples, "two things minus one thing" is grammatical because here the quantity is not "minus one thing" it's the quantity "two things" (plural) joined by the preposition minus with "one thing" (singular).

In the case of the number "minus one" or "negative one", it is plural, because here we have the adjective minus rather than the preposition. "The temperature is minus one degrees". "The bank made an error and deposited negative one dollars into the account".