One thing that makes it obvious that someone is not a native speaker of English is when he uses a regular verb when there is a common phrasal verb that everyone would normally say.

These would be exaggerations, but:

English Learner:  That indeed did fill my heart with fury.

Native speaker:  That really pissed me off.

English Learner: The teacher removed me from the class because I spoke profanely in his presence.

Native Speaker:  The teacher kicked me out of the class because I mouthed off.

English learner:  I certainly erred in a major way, did I not?

Native Speaker:  I really screwed up, didn't I?

I'm not a teacher, just a U.S. native speaker. In my opinion:

You need to learn them as passive vocabulary so that you can understand them when you hear them.

Speaking clear, straightforward English is always good. I do not think you need to use a phrasal verb if you can express your meaning without one. Using English that is more advanced than it needs to be is not an improvement. 

"Why did you have to mention that?" is just as good as "Why did you have to bring that up?"

"I visited him this morning" is just as good as "I called on him this morning."

"I can't give you that information" is just as good as "I can't give out that information."

The term "phrasal verb" is gobbledigook to native speakers, even most learners of other languages.  It's very much an EFL issue.

We would have an instinct about whether or not a word or phrase was formal or informal. So if you used an informal or semi-formal word instead of a phrasal verb, you would often sound natural.

Sometimes the natural alternatives to phrasal verbs would be slang or unusual words and so they might not come to mind e.g. "He went on and on about the football match for hours."   "He spoke" would be correct but sounds too boring and polite for a complaint.  So you could use "rabbited on", or "droned on" which, come to think of it, are prepositional verbs.

Some phrasal verbs are semi-formal e.g. "bring about", so using them in informal contexts would feel out of place. I am not sure if I have helped.

When to add English phrasal verbs, a very tough question.

First, recognize you don't need phrasal verbs to be understood, and it is far more important to be understood than anything else.

Second if you do memorize some phrasal verbs you will probably use them in the wrong way or in the wrong place, once again interfering with being understood.

Every country makes fun of foreign accents and word patterns.  In English the stereotypical foreign guy has an accent, speaks formally, and uses the wrong phrasal verbs and slang expressions.  You probably don't want to be him.

My thoughts are that you really can't learn how to use phrasal verbs properly from a book or a list.  Focus on being understood.  People will forgive your accent and overly formal speech.  Your new English speaking friends will show you how and where to 'lighten up' how you speak with phrasal verbs and expressions.

Have Fun!