Xjyuk

Namo Buddhaya!

Here are my questions regarding justice systems & their morals:

Would it be skillful & moral to report someone to a principle, a police
officer, or any sort of authority when someone is being hurtful to
others (such as killing, bullying, etc.), knowing that reporting them will most likely cause them suffering
e.g. expulsion from school, jail time, etc?

And also is justice skillful, moral and is incarceration moral,
skillful in terms of the Dhamma?

Metta!

Justice system is not skilful, but a necessity to maintain society.

If you are judge you are expected to judge justly.

Reporting crime one needs to weigh the karmic consequences one may willing to bear and impact or betterment it brings.

You might reflect that "beings are heir to their own kamma".

Ideally too it wouldn't be the case in society that "the cure is worse than the disease" -- perhaps it's better, when you're at school, better for a bully and for their victims, that a bully might learn justice and mercy early than not.

Incidentally, one of the Zen stories is The Thief Who Became a Disciple.

I'm not sure what you'd do, in a hypothetical case where you think that the "justice" is unjust.

'Dhamma' means 'that which upholds' society & individual minds.

Without law, there would be chaos & anarchy.

Therefore, it is proper to report criminals.

The Buddha appeared to take it for granted society punishes criminals. For example:

And what, mendicants, is the fear of punishment? It’s when someone
sees that the kings have arrested a bandit, a criminal, and subjected
them to various punishments—whipping, caning, and clubbing; cutting
off hands or feet, or both; cutting off ears or nose, or both; the
‘porridge pot’, the ‘shell-shave’, the ‘demon’s mouth’, the ‘garland
of fire’, the ‘burning hand’, the ‘grass blades’, the ‘bark dress’,
the ‘antelope’, the ‘meat hook’, the ‘coins’, the ‘acid pickle’, the
‘twisting bar’, the ‘straw mat’; being splashed with hot oil, being
fed to the dogs, being impaled alive, and being beheaded.

AN 4.121

Morality in Buddhism is not harming yourself or others. If you make the choice to not report a criminal, this is an act of mental kamma that harms another. The scriptures say:

If you, Rāhula, are desirous of doing a deed with the mind, you should
reflect on that deed of your mind, thus: ‘That deed which I am
desirous of doing with the mind is a deed of my mind that might
conduce to the harm of self and that might conduce to the harm of
others and that might conduce to the harm of both; this deed of mind
is unskilled, its yield is anguish, its result is anguish.’ If you,
Rāhula, reflecting thus, should find: ‘That deed which I am desirous
of doing with the mind is a deed of my mind that might conduce to the
harm of self and that might conduce to the harm of others and that
might conduce to the harm of both; this deed of mind is unskilled, its
yield is anguish, its result is anguish.’, a deed of mind like this,
Rāhula, is certainly not to be done by you. But if you, Rāhula, while
reflecting thus, should find: ‘That deed which I am desirous of doing
with the mind is a deed of my mind that would conduce neither to the
harm of self nor to the harm of others nor to the harm of both; this
deed of mind is skilled, its yield is happy, its result is happy’, a
deed of mind like this, Rāhula, may be done by you.

MN 61

Criminal reap what they sow, as the Buddha taught:

137. He who inflicts violence on those who are unarmed, and offends those who are inoffensive, will soon come upon one of these ten
     states:

138-140 Sharp pain, or disaster, bodily injury, serious illness, or
derangement of mind, trouble from the government, or grave charges,
loss of relatives, or loss of wealth, or houses destroyed by ravaging
fire; upon dissolution of the body that ignorant man is born in hell.

Dhammapada

Buddhism is not Cultural Marxism, which protects the sexual immoral, the creators of pornography, the destroyers of families, genocidal Communists and co-tribal imperialists/colonizers. A Buddhist should not be meek & timid in using whatever moral laws of society are available to them.