I give candidates the option to do a take-home or in-person assessment. For the take-home I communicate that they own everything they produce, and I create an EC2 server for them to use for the interview so that whether or not someone owns a server is not a barrier to entry.

I would definitely decline to continue to interview a candidate if I received this list of demands. The tone is unbelievably entitled and screams "difficult to work with". The suggestion that I would sign an NDA on behalf of my company is absolutely absurd. I would never sign something on behalf of my company without consulting our legal counsel, and I would never continue an interview if I had to involve my legal counsel to determine whether or not a person can code.