Okay.Yes.
Okay.Yes, as long as we understand that "spiritual" is referring to a present reality and not just an intellectual construction.
The term refers to the mediatorial kingdom defined as “(a) the rule of God through divinely chosen representatives who not only speaks and acts for God but also represents people before God; (b) a rule which has special reference to the earth; and (c) having as its mediatorial ruler one who is always a member of the human race.”I'm unfamiliar with the concept of a future "mediatorial" kingdom, so I cannot properly respond.
The mediatorial kingdom is to be contrasted with the universal kingdom, the direct rule of God from heaven over all His creation. (#1 above).
Through creation originally, and now through physical birth, all of mankind is and will be under the universal rule of God. This is in contrast to the spiritual rebirth that is necessary for one to enter the mediatorial kingdom (John 3:3, 5).
The best work on the subject is probably "The Greatness of the Kingdom" by Alva J. McClain, former President of Grace Theological Seminary, Winona Lake, Indiana.