I am definitely not a native speaker, but hopefully what I say will make sense and actually be somewhat correct.
When the form ends with a 'ku', it kinda turns whatever it is attached to into an adverb. It's better to not think of "and" coming after that, in my opinion. The 'kute' lets you say whatever you want after you did something.
Where the confusion comes in, I think is that there is some overlap. I believe if you end something with 'ku', then next thing you say has to relate. For example, "not A, but B". If you end somethin with 'kute', it MAY do that, or it MAY explain the next thing that happened.
Let me try to give an example using your first line there...
買わなく借りました (I didn't buy it, I rented it) (literally: I not-buyingly rented it) Do you see what I mean by 'turns into adverb?
買わなくて家に帰りました (I didn't buy it, and I went home) I could have said here... "I didn't buy it, and then I went to go walk my dog". The 2 things CAN be related, but they don't HAVE to be.
That's why I think it's weird to use "and" in the definition of the first line, when it seems to me that it belongs only in the second line definition. Anyways, this is what I've interpereted. I could be totally wrong haha...