Notes.app - Is it possible to have them both on an account of choice and "On My Mac"?

Are you saying that you want some of your notes only to be on your mac, some to be synced across all devices? You can use the Internet Accounts preference pane to setup accounts to use with Notes. I don't see an option to just limit it to my mac.

Paul

The On My Mac category is inaccessible if you store notes on one or more network servers, such as iCloud, and there are none stored locally.

In the Internet Accounts preference pane, disable all Notes synchronization by unchecking the corresponding box in all mail accounts with which you now sync. The data should be retained on the servers, but it would be wise to back it up anyway by following the instructions in this support article.

Quit and relaunch Notes. The database will be empty. Create a new note. From the View menu, select

Show Folders List

if the list isn't already showing. You should now see On My Mac. Re-enable synchronization. Relaunch Notes again. Your synced notes should reappear.

I am unable to use Notes at all.

Why is that? Many others, including me, have done the same thing without a problem.