Q:

What are the nuances of the verb "to find out"? 

I'm familiar with the different verbs that indicate that someone or something was discovered, noticed, or otherwise taken into consideration (わかる, 知る, 気付く, 見つける, 納得する, 見出す).  However I'm having trouble understanding when to use them. 
The most difficult part is knowing the nuances of conveying that I found out about people or events, so a few general guidelines would be much appreciated. 
In particular, I can think of the following situations:
"I found out about..."

a person, as in "I found out about (aka came across) singer X [and consequently started listening to them]"
a quality of a person, as in "I found out that X was a painter [having known the person but not that s/he was a painter]"
a preference of a person, as in "I finally found out (I learned) he likes his coffee black [after I finally got him to tell me]"
a realization, as in "I found out (aka realized) I don't like wasabi [after finally trying it]" or "I found out (aka noticed) some people dislike Kyary Pamyu Pamyu"
an event related to a person, as in "I found out X got married [having known the person]"
an event in general, as in "I found out they'll demolish that building"
a general fact, as in "I found out that dogs bark" / "I found out that [such] is [such]"
the answer to a question, as in "I finally found out the answer to that question on the test"

This question builds up on this one on Y!A, also asked by me.  I felt I needed to better phrase the question, so here it is. 
Note, I do like wasabi. 

A:

You can't categorize them by what you find out, there are always a lot of options depending on how. 

"I found out about (aka came across) singer X [and consequently started listening to them]"

私はXという歌手を知った
  私はXという歌手に出会った
  私はXという歌手のことを知った - heard by rumor rather than song

"I found out that X was a painter [having known the person but not that s/he was a painter]"

私はXが画家だと（いうことを）知った
  私はXが画家だということを突き止めた - after investigation

"I finally found out (I learned) he likes his coffee black [after I finally got him to tell me]"

私はついに彼がブラックコーヒー派だということを知った
  私はついに彼がブラックコーヒー派だということを知りえた - sounds like a scoop

"I found out (aka realized) I don't like wasabi [after finally trying it]"

私はわさびが苦手だと（いうことが）わかった
  私はわさびが苦手なのだと知った - bookish, reflective

"I found out (aka noticed) some people dislike Kyary Pamyu Pamyu"

私はきゃりーぱみゅぱみゅが嫌いな人もいると知った
  私はきゃりーぱみゅぱみゅが嫌いな人もいると気づいた
  私はきゃりーぱみゅぱみゅが嫌いな人もいるとわかった

"I found out X got married [having known the person]"

私はXが結婚していたことを知った

"I found out they'll demolish that building"

私は（彼らがあの建物を取り壊す／あの建物が取り壊される）ことを知った
  私は（彼らがあの建物を取り壊す／あの建物が取り壊される）ことを突き止めた

"I found out that dogs bark"

私は犬が吠えることを知った
  私は犬が吠えることに気づいた - a valuable discovery

"I finally found out the answer to that question on the test"

私はようやくそのテストの問題の答えがわかった
  私はようやくそのテストの問題の答えにたどりついた - was a long way 

