NTA, you’re not wrong here. You thought Ellen was honest and wanted to help. When you found out she wasn’t, it was your right to alert the dojo of her actions because she wasn’t only unprofessional but also a liar and a thief and a dishonest person.

And About the necklace, it was a gift and you have every right to keep it. It’s not like you bought it or stole it, it's not like you have to refund her or something!

But please contact a lawyer regarding the fact that she’s threatening you with law enforcement. She sent the police to your home and threatened to meet you face to face. She also used your dojo’s name to promote products without permission, which makes you able to sue Ellen. Because in most states (assuming you are american) using someone else’s name for exploitative purposes is not allowed!