Nowadays , more than 99 % Taiwanese can speak Mandarin fluently which is almost the same as China's official language aside from a couple of terms. The nuance is like the difference between British English and American English . It is supposed that if you can speak Mandarin learned in Taiwan , you may well communicate with Chinese speaking people in China . Chinese (Mandarin) is still the official language in Taiwan . 

In terms of Taiwanese ,also popular in Singapore ,  generally speaking , not every Taiwanese (Hokken) can speak fluent Taiwanese notably young people below 40 years old .  I am a fluent Taiwanese speaker and I assume most young people's Taiwanese level is worse than me . It is not easy to find a reliable Taiwanese language partner to practice Taiwanese, though here are lots of language lessons in Taiwan . But I do not think it is practical to learn Taiwanese at the moment while you are traveling in Taiwan especially you are not really living in Taiwan for a long time. If you really want to learn Taiwanese , I may practice speaking and listening with you in Taiwanese . Nevertheless, I am not a qualified Taiwanese(Hokken)  teacher so I would be unable to teach you Taiwanese in a systematic approach.

Thank you each and everyone! 

You've truely helped me! I am so greatful for that.

Thank you again. [:

<3

Mandarin comes with two writing systems, Simplified and Traditional Chinese. What you've been learning is Simplified Chinese, which is the official language in Mainland China. In Taiwan, people use Traditional Chinese. It is not the same as its local dialect called Taiwanese. Almost everyone in Taiwan is fluent in Mandarin, but not everyone is fluent in Taiwanese. Not knowing Taiwanese should not post as a problem in communication. Simplified and Traditional Chinese mainly differ in some characters used. Some words and expressions mainlanders use are not commonly used in Taiwan. How big is the difference? It is hard to quantify. You may think of them as British English and American English. But it is my observation that people from mainland and Taiwan don't find communication with each other a problem. I was born and raised in Taiwan and my Taiwanese leaves a lot to be desired, but if there is any question about Traditional Mandarin please let me know. Taiwanese people are in general well educated, polite, and willing to help others. I am sure you will find plenty of them on this site to help you learn everything that is to be learned in Traditional Chinese and Taiwanese. Good luck!