Hi 淏,
I am not aware of all the rules for making locations into adjectives.
If you want to say Taiwanese, you can. It is an official English. It simply means that you are from the geographic area called Taiwan. It does not mean (or imply) that Taiwan is a separate country.
For example, in America, somebody who lives in the state of Virginia is called a Virginian.
Someone who lives in Texas is called a Texan.
Virginia and Texas are part of the United States.
In France, people who live in Paris are called 'les parisiens'
In French, if somebody says "Je suis parisien(ne)" then that means that the person comes from the geographic area of Paris, the city in France.
People who live in Lyon, France are called "les lyonnais"
If somebody in France says, "Je suis lyonnais(e)", then that means the person comes from the geographic area of Lyon, the city in France.
Texans and Virginias are also Americans. Texas and Virginia are officially part of the United States. No questions asked.
"Les parisiens" and "les lyonnais" are also Frenchmen. Paris and Lyon are officially part of France. No questions asked.
But that's not the reason the words exist in the first place...
Whether or not Taiwan is a separate country or province of China is a political matter. The words "Taiwan" and "taiwanese" are not related to that discussion. Taiwan is the English name given to an island off the coast of China, and taiwanese refers to the people and things that live there.