Grumbler, only GET; and sKull

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Uly, I’m wondering whether it means “to get fixated on smth” or “to learn smth by heart”

Neither. It means to finally understand something. Usually, you say it to someone who doesn’t seem to understand something despite several opportunities:

[mother to son]
— I saw Marjorie and her daughter, Cathy, at the store today. She’s so pretty. She just graduated from college and she’s moving back here to start a veterinary clinic. I think you should call her and…

[son interrupting]
— Mom, when are you going to get it through your (thick) skull that I’m not interested in Cathy?! You’ve been trying to set me up with her since elementary school and I don’t find her the least bit attractive.

To GET SOMETHING INTO ONE’S HEAD is used differently. You use it when someone decides to do something or makes a conclusion about someone or something that you don’t think is right:

— My neighbor is a complete lunatic. He heard my two Russian roommates speaking Russian in the back yard and he’s GOTTEN IT INTO HIS HEAD that we’re all spies. He never says hello, and if we try to talk to him, he totally ignores us. Last year he went as far as to call the FBI!

Thanks Uly, I’ll take a note

I’ll MAKE NOTE of that.
_____________
You’re welcome))

The Brits say “I’ll take a note” 🤷🏻‍♀️
To take a note of smth
However, it may convey a slightly negative, sarcastic connotation.

The Brits say “I’ll make of note of it/that” in this context, just like the Americans. Here’s an Ngram for British English: https://books.google.com/ngrams/graph?content=I%27ll+make+a+note%2CI%27ll+take+a+note&year_start=1800&year_end=2019&corpus=en-GB-2019&smoothing=3

A British friend just told me that TAKE A NOTE OF would sound a little Shakespearean in England, and sure enough, I found this: https://www.dictionary.com/browse/make-a-note-of

Mom, when are you going to get it through your (thick) skull

Is it ok to talk to one's mom like that?!))

Of course. It just means When are you going to finally understand.