The use case is: I need to encrypt data such that only my own private key can be used to decrypt it, from a machine that only knows my public key.
I'd prefer not to have to create and keep track of a sender key pair in addition to my own key pair. I understand that by setting the sender private key to "1" I will not be able to properly authenticate the sender of the message as being myself, but I am happy to accept that.
Related question 1: If a proper sender key pair was used (using a random private key rather than a "1" private key), can the encrypted message be decrypted using only the sender's private key and knowledge of my public key? Edit: Clarification: The receiver (me) would be told the public key of the sender key pair. The crux of the question was about whether if the encrypted message, the sender private key and my public key were all known, could the message be decrypted without my private key?
Related question 2: Is it OK to use the same key pair for both the sender and recipient when using the Box? This would mean a third party can authenticate the message as being encrypted by me, using only the public key.