Father's Lack of Military Service and Relatives' HR

Hi, I am U.S.-born and below the age of majority. I know that my family has HR, but my parents are living in the U.S. and have been for decades. I’m worried about possible complications with applying for a passport and later National ID:

  • My father left Taiwan well before the age of 18, never served in the military, and only ever returned on his U.S. passport, with which he never had any trouble, even when he returned in his 20’s. Will this pose any problems with having his long-expired Taiwanese passport renewed and whether he will have been considered a Taiwanese citzen at the time of my birth (as I was born after he had passed the age to serve in the military)?
  • I have remaining family (aunts and uncles) in Taiwan. Is it legal and possible to have them register me in their HR, though I won’t be living there at this moment?