Translating from Japanese to English 1

The Japanese verbs "shiru," "wakaru."

Shiru: get to know; come to know; find out; find out about; learn; realize; come to realize; notice; recognize; come to be aware of something; etc.

Shitteiru: know; realize; be aware of something/that; etc.

Wakaru: understand; see; get; get to know; figure; figure out; realize; come to realize; recognize; etc.

Wakatteiru: know; understand; be aware of something; be aware that; etc.

"Find out (about)"
I have noticed that "find out (about)" is used almost as often as "know" in English. It may be translated more often as "kizuku," but given that the Japanese "shiru" and "kizuku" are quite similar in meaning, it would be okay to translate "shiru" as "find out (about)" more often than we do.

"Figure out" might be better translated as "rikai-suru" or "mi-i-da-su" (or "mitukeru," as in "kotae wo mitukeru" for "figure out an answer/solution, etc.") than "wakaru," depending on the situation. However, the lines are again blurry.
In English, they say "Figure that out" (imperative) very often. I wonder how best to translate it into Japanese. Obviously, we'd need to translate "I've figured that out" and "Figure that out !"(imperative) differently. "I've figured that out" would be "Wakatta." But "Wakareyo!" sounds a little bit awkward, if not wrong. "Wakattekudasai" isn't any better. "Wakarinasai," "Wakare," etc., are out of question.
"Figure out an answer" could be translated two ways: "kotae wo mitukeru/miidasu" and "kotae ga wakaru (wakatta.)"
For "I figured out how to/a way to ...," "yarikata ga wakatta, " or "Yarikata wo mituketa," would be fine.

The core meaning of "shiru" is get new information about something, or understand something in a new or different way.
The core meaning of "wakaru" is understand something, or find a way to solve something.

"Realize" for "shiru" may not seem quite right, but it depends. "Kizuku" or "wakaru" may be better for it, as in "Don't you realize that?" The fact is, shiru, wakaru, kizuku overlap in meaning. Needless to say the object of a sentence determines which to use.

By the way, "figure out" seems pretty similar to "come up with" in meaning.

It doesn't seem to make a lot of sense to compare English verbs with Japanese counterparts this way, as there is no one-to-one correspondence between them and syntax and things like that have to be taken into account, first and foremost. However, as long as English and Japanese are both human languages, they should have much in common and it would be quite interesting to see how well we can translate from one to the other.