Supreme Court should be nonpartisan. I would remove Presidential appointments since this is putting too much on that critical office. Instead I think this branch should almost be totally separate from others with lower courts promoting members to higher ones.
However, I think there should be an option to call a ballot initiative for people to fire members of the court if they overstep. This wouldn't be a routine thing, just a resource to inject some accountability in an otherwise politically isolated body.
Do you mean having federal court judges elect who is the most qualified among themselves? That might make sense. I guess it would be kind of like the papal selection process.