Yes - I have said this many times to mean "I took care of it." Some examples - your boss asks you if you still have questions about how to file the reports. You can respond with "Yes, I figured it all out" which tells your boss 1) you learned how to do it and 2) you filed the reports. Another example - your wife asks if you requested time off work for your wedding anniversary. You tell her "Yes honey, I got it all figured out" which tells her that yes, you took care of it.

It means that you "understand" everything.

means that he/she knows what will be his/her next move

I don't think so. If you have everything figured out, that just means you know what to do. You may not have "done" what you need to do yet, though. You may not have "taken care" of everything yet.