There are lots of systematic differences between the two standards, but even bigger differences between the way normal people talk. Not being able to put these differences into words is pretty normal unless you’re a trained phonetician. For example, can you put into words the difference between dialects of English? Most native speakers of English can’t do that, at least not using standardised terms.

There are plenty of both academic and lay descriptions of these differences, but starting on Wikipedia is a good idea: https://en.wikipedia.org/wiki/Taiwanese_Mandarin#Pronunciation. Check what it says under “In acrolectal Taiwanese Mandarin:”. Also check the entries regarding different preferred variants and different official pronunciations.

Yes, you are right about that, 研究 is pronounced 就 in Taiwan standard Mandarin.
A number of characters are pronounced differently in Taiwan Mandarin and PRC Mandarin (“Beijing standard”). There are also quite a few words that are different, and some grammar is different as well (use of 有 to mark past tense, different use and position of 了 etc), but you will learn those along the way.

I am not sure what PAVC is, but my teacher friends tell me that the Chinese as a second language departments at big Taiwanese unis try to get people to study in Taiwan even if they later want to use their Mandarin in the PRC and therefore aim to teach PRC standard, although the teachers are all Taiwanese and students will have a hard time understanding and being understood while in Taiwan.

I personally feel that is quite daft, but hey. If you ask the teachers, I am sure they are more than happy to tell you about the Taiwanese way of saying things.