I'm sorry, but what I take from your question is, that you do not understand, why you can only edit the "first so many lines" of your note on your iPhone.
So, I do not know what you are usually used to using, if it's Microsoft OneNote, Google Docs, or a similar service.
Neither do I know if I have understood the issue correctly. But, what I'm taking from your message is, that you intend to use Apple Notes like Microsoft Word or Pages, so with quite some formatting involved.
The thing is, Notes is not designed to work like that. it really is supposed to be used as if you were using a notebook or something in that regard, and you wouldn't start noting something at the bottom of a sheet of paper, would you. so, if you would like to start writing at the bottom of a note, like you would in another program, you can either not, you could use the return key to get down, or you could use said other program.
If that was your issue, I'm sorry I couldn't assist further.
If the problem is that you've got a written note, e.g. from your MacBook, and you are unable to scroll down, that seems like a bug, which could likely be resolved with force restarting the notes application or your Apple device.
If there's some kind of misconception on my side, I'd be happy to be informed about it.