For the first question technically, yes, depending on how you're using it. BUT if speaking to an American the average person might not know what that means. I don't know about England or anywhere else but from my understanding you're better off using recognize as it is the more common word by far. Forget cognize unless it's in English class/University.
Appreciate means more to value
Realize is more "to be/become aware of a fact, reality, something"; to suddenly notice, to notice.
Recognize is more "to be/become familiar with", to know; to acknowledge, show appreciation for (2 diff meanings depending on context)
Appreciate is only comparable to recognize (but are not synonyms) and recognize to realize (can be synonyms but not often depending on the context). Here are examples to distinguish the them:
I realized (noticed) his efforts and appreciated (valued/was thankful for/flattered by) them. I recognized (showed appreciation for) all he's done by agreeing to go on a date.
Recognize vs realize
Do you realize (are you aware) that that's a man?
Do you recognize (are you familiar with) that man?
Appreciate vs recognize
I recognize that man in the picture, it's my dad!
I appreciate all the things my dad has done for me.
^ Very different meanings in that sense
I appreciate (value) all my dad has done for me and recognized (showed appreciation for) his doings by taking him to the mets game.
^ similar but different meanings. What confuses you is that appreciate is in the definition of recognize BUT they're NOT synonyms.
If you try swapping the definitions I put in parenthesis it can help you see the differences because they don't sound to nice. Yes sometimes you can use certain words interchangeably but for the most part these are guidelines of how they are used differently and if you follow them it should help you learn how to use them correctly.