TOOVREN iPhone 11 Wallet Case, iPhone 11 Case Protective Cover with PU Leather Card Holder Adjustable Detachable iPhone Lanyard Stand Strap for iPhone 11 6.1 Inch 2019 Black

Q: Has the manufacturer addressed the issue with the snap falling off?

As far as I know, the manufacturer has done nothing to address this problem. I purchased a small round key chain ring which solved this problem for me.

Q: will this fit over a otterbox defender case?

No, it will not fit over another case since this item comes with its own case.

Q: could I take the lanyard off and switch it with one I have?

Yes you can. There is a metal D ring attached to the leather case. A metal clasp at the end of the strap that is spring locked attaches to the D ring. This clasp is removable if you prefer to use a lanyard.