real number that is strictly less than zero
Negation absolutely is the correct term to use here: it is a synonym of "additive inverse", as noted in the second sentence of its Wikipedia article. This is a well-defined mathematical operation which would absolutely be understood in a numeric context, and is used constantly in math classes from grade school through Master's programs. The dictionary just wasn't providing the domain-specific definition of the term.
The action would be called "Finding the additive inverse" of the number.
The additive inverse is the number that, when added to your initial number, adds up to zero.
There are other possible terms in the Wikipedia excerpt below
In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number), sign change, and negation. For a real number, it reverses its sign: the opposite to a positive number is negative, and the opposite to a negative number is positive. Zero is the additive inverse of itself.
Of note is "opposite number".
The opposite of a number is just the number on the opposite side of zero on the number line.
Yes it's true. If you want to find the opposite just add (or subtract) the number you need to reach 0, in this case +7, and then add (or subtract) +7 again... the result is the opposite. Adding (or subtracting) 2 times itself passing from negative to positive and viceversa is the same of multiplying for -1, where 1 is the neutral number in multiplication.
Yes, that's true. The absolute value of a number is its distance from $0$. With your example, we see that $-7$ is $7$ away from $0$. If we choose to think that $-7$ is to the left of $0$, then the opposite of $-7$ is $7$ to the right of $0$. That would be $+7$.
The multiplicative identity is $1$. The opposite of the multiplicative identity is $-1$. Ergo multiplying by $-1$ gives the opposite of a number.