Is there any way to see if non-friends are interacting with profile or Facebook account?
No, there is no official way to check who has visited or viewed your Facebook profile.
There is a Chrome extension called “Profile Visitors for Facebook”, install it and restart Chrome, open your Facebook account, you will find a new Tab as “Visitors”, there you can find all the viewers who viewed your profile.
Don't trust on any site or app who tell that "See Who Viewed Your Profile", they are fake and phishing sites/apps and can hack your profile or steal your data by asking so many permissions.
:I have not used this extension. Use at your own risk.