No. You do not have unrestricted open work rights. You canāt work legally right now.
However, you havenāt provided enough personal information for us to make a proper assessment, so Iāll just make an example with some basic assumptions.
Letās sayā¦for exampleā¦
Your husband is Iranian. He was hired by a tech company to be a computer science/programmer expert or something. He was sponsored a work-permit by his qualifying company and the associated Alien Resident Card (ARC). He has the right to reside in Taiwan and he has the right to work for that specific company that sponsored his work-permit ONLY. No independent contract work, no starting his own company or self-employment allowed.
Your husband can apply for a dependent based ARC for you to reside in Taiwan based on his work-permit and ARC. Itās assumed that he has already done this and you are already residing here in Taiwan. Once your husbandās job ends and he no longer has a work-permit or ARC, then your dependent ARC is also no longer valid as your status in Taiwan is tied directly to your marriage to your husband and his status in Taiwan.
For now, you may reside in Taiwan, you may cook and clean and take care of your husband and any children that you may have. However, you may not work in any job of any kind for any reason without a work-permit. This also includes any type of unpaid volunteer work or any type of self-employment such as doing nails, eyebrows, babysitting, dog walking, vending, busking, etc. Canāt do any of these unless you receive official permission from the NIA.
You can, based on your education and experience, find a company willing to hire you and sponsor you for a work-permit. Then, you can work for that specific company and perform the duties of the specific job for which you were hired and sponsored. You may not do any private self-employment or start a business or any unpaid volunteer work.
At this point, the only way you can legally work is to have a company sponsor you for a work-permit.
The only way you can start your own business is to jump through the rings of fire that hiring an accountant and/or an attorney could take care of for you. See @Marco who is the duty expert on this.
Remember, what I wrote above assumes your marital status to a non-Taiwan citizen and is just a ball park guess and is not intended to be an all knowing oracle of advice.
Best wishes and welcome to The Flob.
ps. I love your name.