It would probably be a little difficult. Outside of big cities / tourist attractions, I found few people that spoke decent English (thankfully I speak a passable amount of Chinese). The most widespread dialect is Mandarin, but you'll hear a lot of Hokkien and Hakka (for example, transit system announcements).

I found safety to be a non-issue the last time I was there. Taipei feels like any other big Asian city and even on smaller side streets I didn't feel unsafe. In smaller towns and such, I also wasn't nervous.