How do I file a DMCA takedown for a stolen video?

Someone has taken a product demo we paid a freelancer to shoot and is running it on their own store page and in a Facebook ad. Same footage; they have just cropped our logo out of the corner.

I have never filed a takedown before, and I am nervous about getting it wrong and having it thrown out. Three things I am stuck on:

1. Do I need to prove ownership, given a freelancer actually shot it and I only have an invoice?
2. Do I file with the platform or with their hosting provider?
3. Does filing expose me to anything if they push back with a counter notice?

If anyone has a template they have actually used successfully, I would be grateful.