Can the owner see my contacts? I’ve noticed some of my contacts are listed at least three to four times.

Not through family sharing. They may have your email account on their phone in Settings, Contacts, Accounts. Ask them. Or change your email passwords

Duplicate contacts can be caused by having more than one account on your phone with Contacts turned on in Settings, Contacts, Accounts.

I may have Contacts enabled on both my phone and my iPad, but I found that stopping CARDHOP, a program that comes with FANTASTICAL stopped the repetition of contacts creation. I had as many as four copies of many entries in Contacts before I hit on this solution. Eliminating the duplicates has been slow and very frustrating as it has been a strictly manual process, done from the bottom of the Contacts entries up. I had hundreds of duplicates...

For me, the problem began when I upgraded my 3.6 GHz Quad-Core Intel Core i7 iMac (Retina 4K, 21.5-inch, 2017) from Mojave to Monterey and then upgraded my APPs accordingly.

Note: FANTASTICAL is NOT the problem, it is strictly CARDHOP!

Fantastical is an amazingly useful replacement for Finder and I have used it for years before CARDHOP came along, especially this screwed up version of CARDHOP! The Contacts Screwup happened when I upgraded from Mojave to Monterey and continued until I set CARDHOP to NOT open automatically at login (NOTE: both programs, notably CARDHOP, as well as many others were upgraded during the macOS upgrade).

YES I purchased Fantastical. Cardhop is a FREE add-on included with it.