Managing Contacts without linking any accounts
The locations mentioned below where you can find settings may vary across Android versions.


  Did the contacts I manually entered go into HER gmail account? She doesn't need all my personal contacts!


Where do contacts go can be selected with Contacts -> Three dots menu -> Manage contacts -> Default storage location.

Among other options, you have Samsung account (if set), Phone, SIM card, Google (if set), Outlook (if set).
This is exactly what I see in my phone (I have actually three Google accounts).

I guess (did not try it) that if the default storage location is a Google account, and it is removed, the default changes automatically.
So your current setting would be probably not indicative of what it was before.
The best way to check that is entering her gmail account in a web browser, and see if the contacts you added are there.


  Do I have to manually re-enter them, 


If they went to her Google account, you have several options to avoid manually re-entering them. Depending on the number of such contacts, the economics equation on what is most convenient may vary.

You can take advantage of Contacts -> Three dots menu -> Manage contacts -> Import/Export contacts.
I have used that to transfer csv-formatted contacts list from an iPhone to Samsung, avoiding any additional app.


  and if so, how can I be sure that they are being saved to my SIM card? (In case I ever get a new device, it would be nice to simply move the SIM card and keep the contacts.)


See above.

Plus #1: 
You can use Contacts -> Three dots menu -> Settings -> Contacts to show.
You can select any contacts source to be used when showing contacts. You can even select a Custom combined list.
This is what have.
Then, whenever you change the source, you would be showing/hiding contacts, and that can tell you the location of each one.

Plus #2: 
Whenever I Edit a contact, at the top of the screen I see the source of that Contact (Phone, Google, Skype, WhatsApp, etc.)
You should have to tell first the appropriate contact display list as in Plus #1.


  The "read only" contacts are a good mix of ones I want to delete and ones I need to edit (fix misspelled names, add new numbers). How do I manage them? If she un-linked her accounts, why are these "read-only things" still there?


Not sure. Never faced this, but I found a variety of culprit sources of Read-only contacts out there, and correspondingly different solutions.
E.g.
https://www.quora.com/How-do-I-delete-read-only-contacts-from-my-Moto-G2