1.) A mechanical license is not available unless the work has first been published.
2.) Unless you have given the exclusive rights to exploit your work to someone else (e.g. a publishing company, a work-for-hire agreement, etc.), you can always give permission to someone else to use your song for whatever limited or general purpose you deem appropriate. However, if you want to protect them (and yourself) as you say, then you must give them the license to use the work in writing.
3.) Unless the artist who is going to record the song is using a song that is in the public domain or a song that is pre-licensed (e.g. some of the Karaoke-type discs have limited pre-licenses) the recording artist should always obtain a license to use the song no matter what the purpose. It doesn't matter that the intention is only to make a demo. An unlicensed use of the song is a copyright infringement.