Far enough into the 1980’s – I love it! 
To answer Sui’s questions to the best of my knowledge:
Are fines for lateness legal?
If they’re proportional, they should be. There’s also the full attendance bonus. Here’s a legal quirk: if the monthly salary is only the Basic Wage (i.e. less than what most white collar foreigners earn), and the attendance bonus is included in the salary (so it’s not really a bonus), that’s still legal, but deducting the imaginary “bonus” is illegal (unless it’s proportional).
Are fines for taking sick leave or personal leave legal?
Under the Labor Standards Act (applies to most but not all jobs), you get a certain amount of paid sick leave, unpaid personal leave (事假), and other kinds of leave. The Act of Gender Equality in Employment further specifies some of it. A deduction for unpaid leave should be proportional, and if it’s paid or unpaid leave that’s required by law, you can’t lose your attendance bonus because of it.
Is it legal to deduct an hours pay if you are late 5 minutes?
That’s disproportionate, so the answer should be no.
Is it legal to require a person deduct a full hour of sick or personal leave time if they only take a half an hour leave?
Ditto.
In the teaching world, is it legal to require a teacher pay their substitute out of pocket when taking allotted paid personal leave? It feels like this is not really personal leave because you end up paying for a sub, so in truth, there is no “paid” personal leave.
The short answer is no. However, if it’s not statutory leave (under the LSA), I suppose it depends on what the contract says.
Is it legal to deduct a days pay if the school has to provide the substitute, but that substitute does not get paid anything in addition to their normal salary because they did not exceed their normal contracted teaching periods for that week? (In this case, the school is pocketing the money.)
Again, the answer should be no, but if it’s not a statutory requirement, and the contract says you need to pay for it, then I suppose you need to pay for it. Otoh, if the contract says you need to pay what it actually costs the school, and it doesn’t cost the school anything, then it’s 
.
Is it legal to require staff to stay on campus during a lunch break? If you leave for lunch, but come back on time, is it legal to fine for that?
During an unpaid lunch break, not included in your 40 hour work week? That sounds dodgy. The fine sounds like more .
If you are offered a contract with any of these listed and they end up being illegal, how likely is it that you could negotiate those items be removed for your specific contract?
You can negotiate whatever you can negotiate. An illegal clause is an illegal clause, period, and it won’t stand up in court. The statutory minimum requirement trumps the contract. So for example, reducing maternity leave from eight weeks to four is illegal.
Now, an immoral but not quite unambiguously illegal clause, that’s tricky. So for example, a non-competition agreement (before the LSA was amended to address the issue) would typically be found illegal if it didn’t meet certain criteria such as adequate compensation, but the courts sometimes disagreed with each other about that. And when Civil Code Art. 247-1 comes up, the plaintiff may be asked for evidence that the defendant refused to negotiate about the immoral clause (assuming the defendant claims the plaintiff just didn’t want to negotiate).
I would think if you asked for those to be removed or changed, then that company may rescind the job offer on the grounds you are making trouble before even starting the job.
They would probably just make an excuse.
It seems like even if those items are illegal, there is not much that can be done other than passing on the job offer and hunting for a company that actually follows the law.
Keep searching for the promised land. 
