There's some nuanced differences between the two. I came to know implies a more lengthy, substantial or involved process of acquiring knowledge than I learned. Synonyms of come to know include come to understand and become acquainted with, which are a little more distant from learn. For example, I came to know calculus suggests a drawn out process or a deeper, more personal relationship with the subject than I learned.
I don't know of any instances where I learned cannot be validly replaced by I came to know, but I do know that the exchange doesn't always work in the other direction. I came to know my neighbor is fine, but I learned my neighbor is unsemantic (people are not facts or ideas; you cannot learn them). I discount learned a lesson here because it carries a very specific meaning and uses learn in a different sense than usual. Cambridge even lists it as a phrasal verb (or at least thinks it merits a separate entry).
However, your question includes that after both phrases. Having that makes it about some particular pieces of information. In this case, came to know is a superset of learned, because both are completed processes of acquiring knowledge, and learning is about retaining specific facts. Because of this, I can't think of any cases where one works and the other doesn't if you include that.
Regarding your example, what's the context? Was the discovery of this information expedient and easy? Is the sentence intended to be merely informational? If so, use learned. Was it very difficult or time consuming to find out the woman's status? Is it the knowledge extremely important and worth emphasizing? Are you trying to avoid being prosaic? If so, use came to know. Compare:
I flew to Bangladesh to see my cousin. After landing, I went to a restaurant to meet her and her husband. Upon arrival, I learned that she was not in town. She had to make a business trip and would return the following week.
Tracking the billionaire's wife across Europe was no easy task, but I finally found out she was in Madrid, so I double timed it over there. Upon arrival, I came to know that she was not in town. I asked around at the likely clubs and bribed clerks at the upscale hotels, but if anyone had seen her they weren't talking.
In the UK, black person is the usual way to describe someone of African or Caribbean ethnic background and I wouldn't expect it to be taken as offensive. Referring to someone as a black (as a noun) would be offensive.
Referring to someone as the black guy could conceivably be interpreted as a little disrespectful if you might have been expected to call them by name, depending on the context. In your specific example you could have said I don't remember your colleague's name but he's black, if that helps? and I wouldn't expect anyone to be upset by that form of words.
Your friend is either misinformed or engaging in propaganda against perceived "political correctness". Stories about the word "black" being banned in some context or other pop up in the tabloid press with depressing regularity but invariably turn out to be untrue or misreported.
Best Answer
Originally, coining a word, term, or phrase meant that you were creating a new one. More recently (the mid-20th century, according to this article), it took on the meaning of "borrowing" or using a cliché (overused) expression.
So in a sentence like, "Volney F. Warner coined the phrase 'boots on the ground'," we are stating that he invented (i.e. was the first person to use) the term/phrase.
This sentence from a Forbes article has the more recent, contradictory meaning, "Well, this is–to coin a phrase–the 'new normal'," the writer uses "to coin a phrase" to indicate that he is about to use a "borrowed" phrase (i.e. one he didn't invent), the common (and perhaps now cliché) "new normal."
Determining which meaning a speaker/writer intends will depend on the context they use it in; however, the second, newer meaning is typically used in the semi-fixed phrase "to coin a phrase" and occurs right before a well-known (and generally popular to the point of becoming a cliché) expression.