How well is pinyin known in Taiwan?
Not very well known. I lived in Taiwan for a year in 2015, and there were times where I had asked a few Taiwan natives to type words I couldn't understand on my phone. When they saw my phone keyboard input, which was pinyin, they couldn't understand it. Almost all Taiwanese still use bopomofo to type Chinese on their phones. Honestly you don't have to learn bopomofo. Pinyin is easier to learn and the majority of Chinese speakers use it. Just focus on using pinyin, memorizing characters, and speaking to Chinese speakers.