I know that, when it comes to congruence there is no single right answer. But when you are supposed to give result closest to zero, what is the convention?
When dividend and divisor is positive it's simple:
$7\mod{5} = 2$
But when dividend is negative, should it be:
$-7\mod{5} = 3$
or
$-7\mod{5} = -2$
And when divisor is negative:
$7\mod{-5} = 2$
or
$7\mod{-5} = -3$
"Mod" is not normally used as an operator in mathematics; mathematicians write "$7 \equiv 2 \pmod 5$" (meaning "7 is congruent to 2 modulo 5"), not *"$7 \, \mathrm{mod} \, 5 = 2$". The latter notation is not uncommon in computing, however, where it has many applications.
But to answer your question . . . when mathematicians wish to say that an integer p belongs to a certain congruence class modulo a positive integer q, they use that congruence class's representative in the range $[0, q-1]$. For example, they say that $-7 \equiv 3 \pmod 5$, not that $-7 \equiv -2 \pmod 5$, unless they are specifically making the point that $-7$ and $-2$ are in the same congruence class modulo 5. (I think you'll agree that it makes more sense to consistently choose the same representative of each congruence class, rather than choosing a different representative based on whether the integer you're classifying is positive or negative.)
In mathematics, the definition of modular arithmetic assumes a positive modulus, so your questions about negative divisors don't apply. But I think if one were to define a modulus operator such that $7 \, \mathrm{mod} \, 5 = 2$ and $-7 \, \mathrm{mod} \, 5 = 3$, it would be most consistent to define $7 \, \mathrm{mod} \, {-5} = -3$ and $-7 \, \mathrm{mod} \, {-5} = -2$.