I would say, technically they can. However, it's all depends on your company policies.
Specially if your company use MDM and have your device enrolled to Intune. Honestly, I will not suggest you to do so.
Now coming to your questions.
To what extent does the admin have ownership/viewership of the files saved in Office 365 ?
The admin can only do that if he knows your password. But there's something else you need to be aware of is that, the day you leave your company and forget to delete your personal files, then all your data will still be there until your company decide to delete them.
Another thing is that, the admin can also Create a link to view and edit your files.
Is there a way to get a password protected/private space in OneDrive for files that no one but me has access to ?
You can't set another separate password with your OneDrive for business besides the one for your O365 account. So you can only have one password.