Are there areas in Taipei that could be considered something like “Thailand-town”? Places with Thai shopping, Thai restaurants, etc?
In Taipei City not really, but there are a couple very small Thai areas in New Taipei City and Taoyuan.
New Taipei City (in an industrial area), take the MRT to Yongning and take a taxi to “Tai Guo Dian”:
https://www.google.com.tw/maps/@24.9652415,121.4204255,3a,75y,130.54h,81.97t/data=!3m6!1e1!3m4!1sYnnU0e0ydGNsm96hAeKMJw!2e0!7i13312!8i6656?hl=en
New Taipei City (Xinzhuang, a few shops/restaurants scattered on Xinfu Rd.):
https://www.google.com.tw/maps/@25.0492987,121.4669981,3a,75y,236.7h,83.75t/data=!3m6!1e1!3m4!1sallC53VoldNJp56gi2v_pA!2e0!7i13312!8i6656?hl=en
Taoyuan, near the train station:
https://www.google.com.tw/maps/@24.9873233,121.3141362,3a,75y,96.36h,81.98t/data=!3m6!1e1!3m4!1s2ihckmfZdBDu5yx_SC1N3Q!2e0!7i13312!8i6656?hl=en