Sorry, I should have explained this more clearly.
If you are in one of the categories that the Ministry of Labor deems “workers”, the Labor Standards Act applies to your job, so it determines the minimum severance pay and so on, and whenever the contract gives you less than the LSA, the LSA prevails.
If you’re not in one of those categories, the contract prevails (assuming it doesn’t violate any other laws such as the Civil Code, the Labor Insurance Act etc.).
When the contract exceeds the minimum standards set by whatever the applicable law is, the contract prevails.
You can find English translations (sometimes good, sometimes quite sloppy) here – Laws & Regulations Database of The Republic of China (Taiwan) – but it’s a confusing system where this law affects that law and so on, so it’s best to talk to a lawyer or a specialist at the local labor department. The first thing you need to find out is, are you in a category covered by the LSA or not? If the person you ask isn’t sure, mention that the MOL added some (but not all) private school teachers to the list of “workers” a few years ago; it depends on the details of your contract, so bring a copy of the contract with you. If your “school” is technically a buxiban (it happens), then you’re covered.
Regarding taxation, my assessment of the situation is that they’re not doing anything illegal, regardless of your APRC, but of course asking a lawyer is a good idea.
If you can’t reach a settlement with the school on your own, you can ask the labor department to arrange formal mediation (勞資爭議調解). Anyone can request this, whether or not the LSA applies. This is a free service. If both parties reach a settlement during mediation and sign it in the presence of the mediator, that’s the end of the dispute – there will be no trial. If no settlement is reached, at least you walk away with a better understanding of the situation.
You can choose to have someone at the labor department act as the mediator (recommended), or you can ask them to appoint an outside mediator (faster but lower standard of service).
If your medical condition makes it difficult for you to deal with this now, you can come back and deal with it later. Basically, you have two years to make a claim.
If the school has been doing other dodgy stuff, you can file a complaint at the Labor Inspection Office or whatever they’re calling it now. The last time I checked, the New Taipei LIO was out in Tucheng. If you’re going to go down that road, be sure you know what you’re talking about; they want clear and specific violations of the law that are within their mandate and easy to prove.