Translation:Sorry, can I borrow the notes from you?
That's more a property of the English language. Though I do agree that they should change it to 'Sorry, can I...' to minimize confusion.
I believe it's part of the sentence structure for 借/borrow. 向你借something ”向你“ is like "from you" “借" is borrow.
"向你借something" is like "borrow something from you"
"向" can mean "from" per https://resources.allsetlearning.com/chinese/grammar/Expressing_%22towards%22_with_%22xiang%22#Used_as_.22from.22. So, the latter half of the reference sentence is literally "I can from you borrow notes?" and follows a 向 + target + verb pattern.
Because the notebook here has a possession state which is "your",therefore you cant say can i borrow a notebook.
'Excuse me. Can I borrow your notes please' was wrong. Punished for being polite again I guess...
This one expresses more polite. It sounds like you wanna borrow something from the stranger. The way between friends should be 我可以借你筆記嗎
Though this sentence gramatically means 2 opposite questions. But only can I borrow your note is frequently used. If you don't want confuse yourself, put 的 then becomes 你的筆記 is more clear.
By the way, here 跟 can substitute 向, 我可以跟你借筆記嗎 is also polite speaking. 向 is too polite not used often nowadays.