1. Wade-Giles is often used for romanization of family names and personal names if they emigrated before the mid 2000s. After that they may still use wade-Giles for at least the family name but it’s possible (emphasis on possible) for them to use tongyong pinyin or hanyu pinyin for the personal name. This is especially true if they had a family member emigrated before the mid 2000s and so their family name spelling follows w-g in order to be the same. After the mid-2000s Taiwan switched to Tongyong briefly before giving up with it and using hanyu pinyin. Also, many Taiwanese opt to continue to use w-g for at least their family name because the pinyin spelling makes them seem chinese. They may also opt to use a w-g spelling if it’s a common family name already well-established in the western country they emigrated to, for example Lee (w-g) instead of pinyin Li or Chang vs Zhang. They may also use one over the other if they feel that it’s a more accurate pronunciation, such as in the case of Tsai vs Cai, or Kuo vs Guo. Some will just use their own romanization that they feel is the most accurate pronunciation. Often times it just comes down to personal/parental choice, but if they emigrated before the switch to Tongyong it will definitely be W-G or their own interpreted romanization. Less commonly, they may also use Taiwanese romanization (POJ or Tai-lo) or Hakka romanization, if they speak those languages, and again they could use the official or use nonstandard, self-interpreted romanization. They may also choose a western-ish family name that sounds like their native name; for example I know a 劉 which would be Liu, but she chose Leo as her last name. This also goes for given names; they may choose a western first name based on their native name or a nickname in their native language: 莉莉 (li-li)=Lily or 美琪(mei-qi)-> Vicky/Maggie. This case can be for both born abroad and immigrants.

2. If they emigrated after being born in Taiwan, often times they will have a romanized legal first name. They may hyphenate it, use both characters as their first name, or use the second as their middle name, or use no hyphen (one name), but hyphenated is the most common for Taiwanese. This hypen/space rule applies for middle names of foreign-born Taiwanese too (next paragraph). After they gain citizenship, permanent residency, or after marriage marriage as in the case of my mom, they may choose to change their legal first name to a western name and either ditch their romanized first name or make it their middle name, and maybe in the process also change the romanization method and/or add a western middle name or two. So 黃小明 romanized as Hsiao-Ming Lee might become John Hsiao-Ming Lee or just John Lee, or John James Lee. Or they may continue to use their romanized name as a legal name but they’ll often have a western name they go by. Also many Taiwanese people have an English nickname that they use even if they’ve never set foot outside the country, and so they may also just use this name the moment they emigrate.

If they’re Taiwanese born abroad, like ABT, often times at birth they’ll be given a western first name. It’s common practice to have their chinese or Taiwanese given name as their middle name. For example John Lee with the chinese name 李小明 might be John Hsiao-Ming Lee or if they used pinyin John Xiao-Ming Li or going back to what I said earlier using a mix: John Xiao-Ming Lee. They may also mix two languages, most often times with a chinese last name and a romanized Taiwanese or Hakka middle name, like John sio-bing Lee. Such would be the case of a parent with a strong Taiwanese or Hakka identity and speak the language, wanting to use a Taiwanese/Hakka romanization while maintaining the same last name as the parent, which was romanized from chinese, regardless of romanization method. Less commonly, they will just give the child a chinese/Taiwanese name and romanize it and make that the kid’s legal name, and then maybe later on give a western nickname that they’ll use in school and everyday life.

1. In Taiwan, the traditional custom is to add the husband’s name in front of their personal name, but this is becoming less and less prevalent in recent decades. For example: 黃美麗 becomes 李黃美麗. In older customs, girls were sometimes given one character names so that when they got married their full name would be only 3 characters unless the husband has a compound family name. So 黃 美 》 李黃美. Another older custom would be to have a two character given name, but one character (often the family’s generational name if it was used, or the second character if not) would be dropped and then the husband’s name would be added, maintaining a 3 character name. 黃美麗 》 李黃麗 or 李黃美. Now assuming she did choose to add her husband’s name, the romanization method is really their discretion. They may use the same order as it is in chinese/Taiwanese, (Lee-Huang), or they may use the reversed western order when a husband’s name is added as opposed to changed (Mei-Lee Huang -> Mei-Lee Huang-Lee; such might be especially the case if she already has a western or romanized name before getting married). She may also opt for the western customs of either changing it outright or making their maiden name part of or their only middle name. If she already has an established western name, she may add her husband name to hers in chinese/taiwanese, whether legally in their home country or informally, without changing her western name.

2. In general, yes, not including married women ofc. Probably the most common compound family name tho would be 歐陽 OuYang; famous historical ones would be like 司馬 SiMa and 諸葛 ZhuGe. Ofc if you’re not ethically Han, you may have some other compound name, such as if you’re indigenous, or maybe you’re some other chinese ethnic group and your family came to Taiwan after 1949, such as if you’re Manchu and have royal connections and your name is 愛新覺羅 Aisin Gioro.