General confussion with the 承る family

I’m a little confused with the meaning of these three words: 承認、了承、承る.
After checking some dics and sites on the internet this is what I have:

承認 :
To recognize something that has been justified or it’s a fact (like “approved” or “checked and confirmed”). It’s also usually used by a company or corporation (possible synonyms: 認める、OKです).

了承:
To be completely convinced about the circumstances of something. I don’t understand this one, but I think It could be something like “there is a plan or a schedule being the object of a discussion and finally, It gets approved”.

承る:
To know something only by rumors or “what my friend told me”, but it’s not a fact neither something I truly understand.

bonus:

承知:
To understand or comprehend something very very well. Possible synonyms: よくわかる、知る、心得る、理解.

I’ve read tons of example sentences but I am not sure of having understood completely all the meanings.

Thanks in advance~

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I’m not really sure where this is coming from, but maybe it’s someone’s interpretation of the fact that 承る can be used as a kenjougo (humble language) form of 聞く.

I’ll say, that is not a common way to encounter it. Every time I have ever seen it used, it was the “take a reservation or order” meaning in retail situations.

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I don’t think there’s any notion of “completely” in this word. My dictionary gives something of the effect of “listen to a situation/circumstances and understand/agree/consent (納得)”

@Leebo already explained 承る

To understand is only one of the definitions of (the する form of) that word. I don’t know why you added “very well”